People always forget about radiation when they imagine space colonies. Out there, on other worlds, humans won't be shielded from cosmic radiation the way we are by Earth's magnetic field. That's why cities on other worlds are likely to be underground. Here are few places we might build them.
Above you can see a HiRISE image of an unusual Martian feature — a crater with a hole in the bottom on the slope of the volcano Pavonis Mons. According to researchers who imaged the feature:
The dark spot turned out to be a "skylight," an opening to an underground cavern, that is 35 meters (115 feet) across. Caves often form in volcanic regions like this when lava flows solidify on top, but keep flowing underneath their solid crust. These, now underground, rivers of lava can then drain away leaving the tube they flowed through empty. We can use the shadow cast on the floor of the pit to calculate that it is about 20 meters (65 feet) deep.
This is precisely the kind of place we'll want to found future cities on Mars. The planet has a weak magnetic field that allows much more radiation to hit the ground than we get on Earth. People who live there will need a layer of rock to protect them from these energetic particles if they don't want to become sterile or develop cancer.
Here's another Martian lava tube entrance, in Tractus Fossae, from HiRISE data.
Maybe we'll colonize one of these underground caverns, and cap it off with an installation that looks a lot like this one, from an image of an underground Martian city by temnobelos
Closer to home, the Moon has a number of ancient lava tubes left over from the days when it was a much more fiery world. NASA has already suggested that an old lava tube, basically an underground tunnel, would be ideal for building on the Moon. There is no atmosphere and very little magnetic field to protect Moon colonists from radiation, so life there would be mostly underground — or in facilities that are heavily shielded. It's much cheaper to use rock to block radiation than build shielding, though. Above, you can see a collapsed lava tube on the Moon (via NASA/GSFC/Arizona State University) — there is actually a small bridge of land between the two holes, which let us peek into the long lava tube.
Another lunar lava tube entrance, via NASA/GSFC/Arizona State University
Ultimately, an underground lunar city might look something like this concept art by John Eaves — half buried, with a few bits poking up above the lava tunnels.
Moving beyond Mars into the asteroid belt, we might build cities inside asteroids, with just a few features outside the asteroid to indicate there is life within. (image via Star Wars: The Galactic Commands)
We might start with an asteroid like 243 Ida (picture via NASA/JPL), which is about 35 miles long and even has its own moon. It sits between Mars and Jupiter in the asteroid belt. We'd core it and spin it to induce gravity on the interior walls. Imagine living on the inside of a spinning asteroid tube, with your city arcing over your head, and the centrifugal forces keeping your feet planted on the ground.
It might look something like this (but without the big windows).
Beyond the asteroid belt, another possible radiation-shielded spot is Jupiter's moon Europa. It's completely covered in a thick layer of ice, riddled with cracks (those are the reddish lines you see). This ice protects enormous, warm oceans below from cosmic radiation. So life might be thriving beneath this protective crust — and humans might one day thrive there too.
From NASA, we have this gorgeous concept art of Europa's icy crust. The crust itself is full of hidden lakes and riddled with geysers that spout up from the relatively warm seas that lurk below. These features are what create the crazed, cracked surface of Europa.
The artist Vili (Velislav) offers us one vision of humanity's first visit to Europa's icy caverns over the covered oceans.
Beyond Jupiter, there are a few possible places we might be shielded — Saturn's moon Titan (illustrated here by Ron Miller) has a thick atmosphere, but still gets a lot of radiation bombardment on the surface. As for gas giants like Jupiter, Saturn, Uranus and Neptune — well, there isn't a solid surface for us to colonize. So you might see fantastical floating cities, heavily shielded from radiation, but that would require technologies far beyond even the ones that would allow us to build shelters in the lava tunnels of Mars and the Moon.
Of course there's always the possibility that we will re-engineer humans to be radiation resistant, and we'll dwell anywhere in space we want, without fear of developing cancers or other conditions. (Illustration of a General Systems Vehicle by Luke Frost)