In orbit, not on a planet or moon. Why should we live in orbit rather than on a planet or moon? Because orbit is far superior to the Moon and Mars for colonization, and other planets and moons are too hot, too far away, and/or have no solid surface.
For an alternate view, see
Robert Zubrin's powerful case for Mars exploration and
colonization. Mars' biggest advantage is that all the materials necessary for life may be found on Mars. While materials for orbital colonies must be imported from the Moon or Near Earth Objects (NEO's -- asteroids and comets), there are many advantages to orbital colonies. Advantages include:
The best place to live on Mars is not nearly as nice as the most miserable part of Siberia. Mars is far colder, you can't go outside without a space suit, and it's a months-long rocket ride if you want a Hawaiin vacation. The Moon is even colder at night, and it's literally boiling during the day. By contrast, orbital colonies have unique and desirable properties, particularly 0g recreation and great views. Building and maintaining orbital colonies should be quite a bit easier than similar sized homesteads on the Moon and Mars. Colonies in orbit are better positioned to provide goods and services to Earth. For these reasons, orbital colonies will almost certainly come first, with lunar and martian colonization later.
- Earth-normal 'gravity'. The Moon and Mars have a surface gravity much less than Earth normal (which called 1g - the g stands for 'gravity'). The lunar surface is at roughly 1/6g and Mars is a 1/3g planet. Children raised in low-g cannot be expected to develop bones and muscles strong enough to visit Earth except in desperation -- it will be too painful and exhausting. For example, this author weighs 73kg (160 pounds). If I went to a 3g planet, the equivalent of moving from Mars to Earth, I would weigh 225 kg (almost 500 pounds) and would have great difficulty getting out of bed. For children raised on the Moon or Mars, attending college on Earth will be out of the question.
By contrast, orbital colonies can rotate to provide any g level desired, although it's not true gravity. Spinning the colony creates a force called pseudo-gravity, that feels a lot like gravity. Pseudo-gravity is much like what you feel when a car takes a sharp turn at high speed. Your body is pressed up against the door. Simillarly, as an orbital space colony turns, the inside of the colony pushes on the inhabitants forcing them to go around. The amount of this force can be controlled and for reasonable colony sizes and rotation rates the force can be about 1g. For example, a colony with an 895 meter (a bit less than 1000 yards) radius rotating at one rpm (rotations per minute) provides 1g at the hull. Children raised on orbital colonies should have no trouble visiting Earth for extended periods.
- Rapid resupply from Earth. The Moon is a few days away from Earth, and trips to Mars take many months. Early colonies in Earth orbit will be only hours away. This is a huge logistical advantage for a large project like building space settlements.
- Continuous, ample, reliable solar energy. In orbit there is no night. Solar power is available 24/7. Most places on the Moon or Mars are in darkness half of the time (the only exception is the lunar poles). Mars, in addition, is much farther from the Sun and so receives about half the solar power available at Earth orbit. Mars also has dust storms which interfere with solar power.
- Great views from Earth (and eventually other planets). Space colonization is, at its core, a real estate business. The value of real estate is determined by many things, including "the view." Any space settlement will have a magnificient view of the stars at night. Any settlement on the Moon or Mars will also have a view of unchanging, starkly beautiful, dead-as-a-doornail, rock strewn surface. However, settlements in earth orbit will have one of the most stunning views in our solar system - the living, ever-changing Earth.
- Weightless recreation. Although space colonies will have 1g at the hull, in the center you will experience weightlessness. If you've ever jumped off a diving board, you've been weightless. It's the feeling you have after jumping and before you hit the water. The difference in a space colony is that the feeling will last for as long as you like. If you've ever seen videos of astronauts playing in 0g, you know that weightlessness is fun. Acrobatics, sports and dance go to a new level when constraints of gravity are removed. It's not going to be easy to keep the kids in 1g areas enough to satisfy Mom and Dad that their bones will be strong enough for a visit to Disneyland.
- Zero-g construction means bigger colonies. Space colonists will spend almost all of their time indoors. It is impossible for an unprotected human to survive outside for more than few seconds. In this situation, obviously bigger colonies are better. Colonies on the Moon or Mars won't be much bigger than buildings on Earth, especially at first. However, in orbit astronauts can easily move spacecraft weighing many tons by hand. Everything is weightless and this makes large scale construction much easier. Colonies can be made so large that, even though you are really inside, it feels like the out-of-doors.
- Much greater growth potential. The Moon and Mars together have a surface area roughly the size of Earth. But if the single largest asteroid (Ceres) were to be used to build orbital space colonies, the total living area created would be approximately 150 times the surface area of the Earth. Since much of the Earth is ocean or sparsely inhabited, settlements built from Ceres alone could provide uncrowded homes for more than a trillion people.
- Economics. Near-Earth orbital colonies can service Earth's tourist, energy, and materials markets more easily than the Moon. Mars is too far away to easily trade with Earth. Space colonies, wherever they are built, will be very expensive. Supplying Earth with valuable goods and services will be critical to paying for colonization.
Mars and the Moon have one big advantage over most orbits: there's plenty of materials. However, this advantage is eliminated by simply building orbital settlements next to asteroids. It may even be easier to mine asteroids for materials than the Mars or the Moon as there is much less gravity. Fortunately, there are tens of thousands of suitable asteroids in orbits near that of Earth alone, and far more in the asteroid belt. Early settlements can be expected to orbit the Earth.
Later settlements can spread out across the solar system, taking advantage of the water in Jupiter's moons or exploiting the easily available materials of the asteroid belt. Eventually the solar system will become too crowded, and some settlements will head for nearby stars.
Interstellar travel seems impractical due to long travel times. But what if you lived in space settlements for fifty generations? Do you really care if your settlement is near our Sun or in transit to Alpha Centuri? So what if the trip takes a few generations? If energy and make up materials for the trip can be stored, a stable population can migrate to nearby stars. At the new star, local materials and energy can be used to build new settlements and resume population growth.