The Solar System
The year is 2162 of the Common Era. Human civilisation and its evolving artificial and biological sapient offshoots are spreading across the Solar System and are partially unified under the Solar Federation.
The Solar Federation is a cosmopolitan interplanetary alliance with a similar role to the United Nations of mid-20th century Earth, however with greater representative imput and relevance. The formation of the SF was the result of the United Nations of Earth, Lunar Confederation and several independent Near Earth Orbit settlements ratifying the SF Charter and the Pan-Sapients Rights Accord at the Armstrong City Summit on Luna. Since then other polities including the Republic of Ceres, Asteroid Belt Alliance and Association of Jovian Polities have become signatories. The chief executive of the SF is the Secretary-General. The governments of each member polity has a vote in the Polity Council and each member citizen has access to the Solar Assembly, the largest participatory e-democracy ever to have existed. The SF is responsible for pan-system agencies such as the Interplanetary Space Guard which is a search and rescue and space travel regulatory organisation and the Solar Intelligence Agency, a covert body (often working in partnership with the United Nations Security Bureau) responsible for protecting civilisation from existential risks and violations of the PSRA obligations of member polities.
Here is a brief list of major settlements and polities across the Sol System.
(Note: a thank you to Jave Harron for helping put together these lists).
Sol and Mercury: Aside from a few minor research habitats and solar plants, there's nothing quite interesting around the sun. Now, Mercury, however, is a completely different beast. It's a major world for industry, the vast majority of it run by AGIs, uploads, and other infomorphs. Aside from solar collectors, mines, and anti-matter production plants, Mercury is an uninteresting little hell-ball. The amat plants have security more akin to a military base, since there's huge potential for destruction there if certain unsavory elements overtake such a facility.
Venus: Officially designated the Venus Colony. This is a UNE Extraterrestrial Mandate Territory undergoing a 1,000 year terraforming project.
Venus is to the inner solar system to what Antarctica was to 20th century Earth, only more interesting. The thick atmosphere and proximity to Sol make its surface a pressure cooker for most types of machinery and protective equipment. Only the most durable technologies can survive on the surface, so don't bother bringing fragile nanotech or electronics along. The natural hazards are real killer and include pools of acid on the ground, lightning strikes hotter than the sun, and sulfuric acid in the atmosphere. This is the sort of hellscape that would make the Devil look for better real estate. A few rugged structures dot the surface, mostly unmanned mining colonies and a few research outposts. There's a few "unofficial" habitats for people seeking solitude, and they don't like visitors. This is one place someone can go to vanish for good, or send evidence to vanish for good. Of note, however, are the aeropoli, floating cities in the upper atmosphere. Suspended by redundant "vac-sacks" (bags of literal vacuum), the cities float at a point of the atmosphere that's got the same exterior pressure as Earth, about 50 kliks above the surface. So far, these are a trendy get-away and hot real estate (no pun intended) for the eccentric and daring, but the idea of living above a pressure-cooker hellhole of a planet is more than enough for most people.
Earth: The United Nations of Earth is the official central governing body of the planet Earth and subsequently the most powerful government in the Solar System, however much of its powers are decentralised among regional blocs and member nations. The SF modelled its administration on the UNE with the World Assembly and Security Council. The most powerful leader in the Solar System is the President of the United Nations of Earth who is aided by a Global Executive. The incumbent President of 2162 is Muhammad NOORZAI, a Pakistani citizen. The location of UNE bodies and therefore de facto world capital is Nairobi in African Union-Kenya, chosen for its location close to the birth place of the human species.
Earth is the cradle of humanity, and still a complete and utter shithole in a lot of places (which we've helped turn it into). As a note, sadly, New Jersey still hasn't been flattened from orbit. Pollution, overuse of resources, war, and other favorite human activities has turned parts of our home into glorified garbage dumps. Take a look at the desertification in Africa, the Americas, Asia, and even parts of Europe. Mother Nature's wounded and gone mad. The vast majority of the population lives in cities. A few sealed cities, arcologies, have been set up in more remote regions as a response to the crappy climate. Outside, though, are expanses of slums built into the old suburbs that go on for kilometers in all directions. Of course, the nicer cities have urban farms, preserved (or restored) wilderness, and green suburbs and mass transit, but there's still plenty of crappy parts of Earth. If you've got money, chances are you'll be living in a walled, self-sufficient arcology, with plenty of cheap labor. Earth and many stations are technically united under the United Nations of Earth. While it's (mostly) democratic, it serves the old moneyed interests without fail. The UNE recently helped unite most of the major nations and blocs of Earth (example European Union, North American Union, Association of South East Asian Nations etc), a move that did not go completely unopposed. The Regionalist Wars of the 2140s and 2150s were guerrilla operations, low-level warfare, and counterinsurgency campaigns against people who opposed joining the UNE. Their official spin is that these were all backwards dictatorships, religious and nationalist fanatics, terrorists, and xenophobes lashing out at the rest of the world. Now, don't get me wrong. The UNE brought democracy to a lot of places where it wasn't before, but they did it in a hamfisted, sometimes brutal way that allowed certain business interests with political connections to benefit greatly. There's still a lot of festering wounds because of it, both from the groups who got crushed (even if some of them deserved it) and a lot of the vets, who ranged from conscripts to volunteers to professionals to mercenaries. A number of refugees and disenchanted groups have headed for the stars afterwards, often leaving their old assets in the hands of the UNE's patsies. Note the Regionalist Wars did ignore a number of micronations, nasty states, and the like that withdrew or voted against such activities when the passed the Stabilisation Resolution (which started off the whole thing). Best not to discuss it if you're ever in one of those regions. Some places are ticking time bombs, and a few people are hoping they go off.
Luna: Officially the Lunar Confederation. The capital and location of the Solar Federation headquarters and facilities are Armstrong City.
Luna or The Moon is the location of humanity's baby steps into space. It's got plenty of minerals and helium. It's also home to several well fortified, easily defensible underground settlements. From Armstrong City to the Chang'e Industrial Warrens, building underground was a decision that made it easy to avoid meteors and space radiation. Armstrong City is the major residential area of the moon (built around the preserved historical landing site). The Americans helped build the complex, but it eventually became dominated by a group of Texan libertarian transhumanists, the Textropians. Now, it's somewhere between an anarcho-capitalist "state" and minarchist libertarian one. Most things are legal, and it's run by a group of non-profit civic trusts. While high power weapons are frowned on, they do hand out rubber bullet shooting firearms (often made to resemble vintage Wild West designs) to most guests and give free lessons. The Textropians make a killing on their tourism business, since the low gravity of Luna means jet pack rides are economically viable. On the other side of the moon, there's a Chinese mining complex that grew into a decently sized city, the Chang'e Industrial Warrens. Unlike the crime filled hellhole that is New Shanghai on Mars, the "Industrial" Warrens are quite green. Low gravity, repurposed industrial infrastructure, and bioengineered plant-life make for a green, and wide-open seeming city. The city became more cosmopolitian as people from across Earth moved on to it. It still remains a key space port on Luna.
Mars: Officially the Mars Colony. This is a UNE Extraterrestrial Mandate Territory undergoing a 500 year terraforming project. The financial backing of the project is the UNE and a private partnership with the massive mulitnational Martian Development Consortium. The current UNE Governor of Mars is Terrance KHAN of North American Union-Canada extraction. It is expected that Mars shall become an independent polity before the 23rd century.
Mars is prime cosmic real-estate. It has a 24 hour day, geothermal energy, and an environment that is easier to terraform than Earth. It's also right next door to our old home. Drawbacks include an atmosphere we can't breathe, a lack of shielding of cosmic radiation and space debris, and less gravity (a drawback to some). Currently, it's being terraformed by some von Neumann robots planting and seeding the place with bio-engineered life to help provide an atmosphere. Specifically, I believe the planet's being seeded with different types of bioengineered, radiant resistant lichens (a hardy combination of fungi and algal cell found in harsh environments here on Earth). There are a few nice locations here, most involving fields of rocks in all directions. There are some major settlements on Mars, and there are more people here than Venus. The colonial capital and the main hub of research, industry, terraforming, and coordination of all of them is Olympia. It's constructed in the crater of Olympus Mons, a (thankfully extinct) volcano and the highest peak in the inner system. Consisting of several habitats connected underground, Olympia ranges from lush greenhouses and bio-domes to sleek labs to gritty infrastructure and mines. Another major settlement is New Shanghai, a Chinese settlement that's effectively ruled by crime bosses. Despite being a major smuggling outpost, they are a lucrative port city with many well-connected beneficiaries.
Asteroids: The Belt isn't as densely packed as old science fiction would have you believe. The rocks are floating hundreds of kilometers apart in space. Don't let that fool you, however, these rocks are still full of plenty of danger. Ever considered the fact there may be radiation or swarms of space debris coming at you from unseen angles? Then there's also some of the locals. The belt is a nice spot to mine for raw materials, and many habitats are constructed out here. Contrary to the stereotypes of tough asteroid miners, the vast majority of miners are lazy bastards and infomorphs content to let near brainless bots carve up the asteroids for them and ensuring everything's working fine. And if something isn't, they send out another brainless bot to fix it. Asteroid miners do have hardships and hazards, though, from collisions with errant spacecraft to malfunctions of all sorts. There are some pirate attacks out here. Typically, an armed space craft assaults an asteroid, snatches a load of equipment or minerals, and flees. Most of the time, the pirates aren't even opposed, since the miners just file a report and request replacements (or just locally manufacture some more). And on more than one occasion, the miners are in league with the looters. Most asteroid miners aren't the tough blue collar types you see in the media (although a handful are), but instead some bureaucrat who's pissed off their boss somehow.
There is one organised polity in the Belt, the Asteroid Belt Alliance. This is a loose grouping of independent Belt settlements that joined together to vie for influence in the Solar Federation. The ABA government meets in the largest asteroid settlement, Pallas.
Jovian System: This is one of the more interesting cases. Jupiter's a big resource, and lots of people seek to claim a part of the pie. (Especially when the pie consists of prime fusion grade hydrogen.) To add to the chaos, a number of conflicting claims lie on the ice moon, Europa, with its potential life under the icy crust. From corporations and polities with conflicting claims, everyone wants something here. While the radiation is a killer, a number of shielded craft work in the (upper) atmosphere of Jupiter. There are a number of helium and hydrogen "scoop ships" patrolling the area, recovering fuel for reactors across the solar system. A few vac-sack airships also patrol Jupiter, including a few pirate vessels. However, there is a habitat of note near the Jovian system (but thankfully well shielded from its radiation). The nice-sized colony of New Antioch on Ganymede is a religious retreat holding members from all around Earth and the inner system.
Outer System: Out past the Jovian system, population density drops off fast. There are a few interesting things in the outer system. Saturn's moon Titan (officially a UNE Extraterrestrial Mandate Territory) has a research base that's growing fast, and a number of scoop ships are investigating using the other planets as raw materials (although transit times are a bitch). There's some AGI-run automated craft and habitats near the edge of the system, and even a few habitats hiding their emissions as much as they can. An alliance of remote settlements on Saturn's moon Iapetus has set up an anarchist society based on the philosophy of Ukrainian revolutionary Nestor Makhno, and they go by the name "the Nest."
Exoplanets: Aside from some AGI-run or upload-run von Neumann and seeder ships, not many probes or craft have been launched outside the solar system. The communications delay of a few years due to the speed of light means laser, radio, or neutrino communications would making keeping touch a real pain in the ass. Of course, it will be while before we hear anything back, since most of the craft have not even arrived in their respective systems, so it will be a while before we hear if the mission is even successful. (If we hear back, that is.) Even though extrasolar colonization is a favorite topic among spacecraft manufacturing groups, policy makers, and science fiction nerds, the bulk of civilization's still focused around the Sol System and Earth, and will be for the foreseeable future.