There five important factors for long term human space colonization:
Resources - humans need certain kinds of resources to survive and continue a technological civilization: carbon, nitrogen, oxygen, hydrogen, silicon, metals. We also need energy: solar, nuclear, or geothermal.
Accessibility - this is what people often mean when you say "gravity well". How much energy does it cost to get there or leave there? Imagine you live on your own personal island. Sure, it's quiet and there's no neighbors to annoy you, but if you don't have fuel for your helicopter or a nice speedboat your economic sphere of influence will be significantly constrained.. much as we are down here on Earth.
Radiation Protection - also, down here on Earth, we have an atmosphere that protects us from the harsh solar and galactic cosmic radiation, but just about everywhere else in the solar system we're going to have to make do with a more substantial physical barrier - either thick metal plates or, more likely, a couple of meters of dirt.
Gravity - we evolved in a 1g gravity field and all the evidence we have so far indicates that we may indeed need that much gravity - particularly for having offspring. Perhaps we can get by with less, but there's no evidence for that yet.
Technology - this basically comes down to when we go. Our current technological capabilities are insufficient to get beyond cislunar space. Soon we should be able to go anywhere in the inner solar system. Eventually, we'll be able to go anywhere in the solar system and then it'll just be down to delta-v requirements. Some day, the stars.
So let's consider the possibilities. To give an objective analysis of the suitability of each destination I'll adopt a scoring system where 2 points are awarded if something is particularly favorable and comes as an inherit part of the destination. If some application of existing or near-future technology is required then a score of only 1 point will be awarded. I wont score the technological requirements to reach the destination as we will only be considering destinations that are reachable with current or near-future technology.
Score: 1 Res, 0 Acc, 2 Rad, 2 Gra = 5.
Although we're talking about a new home for humanity, I think scoring our current home is a good way to show the motivation to leave it. We certainly had plenty of resources on this planet, but there's also a heck of a lot of us on it now and the availability of those resources is starting to dwindle. The accessibility of Earth is the worst in the inner solar system.. it takes so much delta-v to get off it that we have to use multi-staged rockets. The radiation protection is exquisite, and so is the gravity.
Score: 0 Res, 2 Acc, 0 Rad, 1 Gra +1 Zero-G Bonus = 4.
The traditional O'Neill Colony, Clarke Wheel, or even the ISS imports all its resources. Of course, the accessibility is great but as a result of the high cost of import there's few materials to use for effective radiation shielding. Artificial gravity can be provided, and the easy access to zero-g is a bonus to scientific work.
Score: 1 Res, 1 Acc, 1 Rad, 0 Gra = 3.
The Earth's Moon is often considered a barren destination with little in the way of resources. This picture has been disputed over the years with many people pointing out the wide availability of metals, silicon and oxygen in the lunar regolith. Recently, the discovery of a water cycle on the Moon and the expectation that there may be as much carbon as there is hydrogen firmly busts the "desolation" myth. That said, it certainly will be a lot of hard work to live there. The accessibility is poor, but not nearly as bad as Earth. Radiation protection would be of the underground variety. The gravity is terrible for human reproduction and there's nothing we can do about it.
Score: 1 Res, 0 Acc, 2 Rad, 2 Gra = 5.
Colonizing the surface of Venus is mostly out of the question due to the surface temperature and pressure (460C and 93 atm). Although it may be possible to colonize Venus with platforms floating in the upper atmosphere, the only resources available would be the toxic atmosphere and anything you can collect, with great expense, from the surface. And the gravity well is almost as bad as the Earth. Radiation protection from the atmosphere alone would be same as Earth, but the magnetic field is much weaker. Venus also has another thing going for it: it's the only body other than Earth in the inner solar system which has a near-one gravity.
Score: 2 Res, 1 Acc, 1 Rad, 0 Gra = 4.
Mars is almost universally considered the premier destination for human expansion into the solar system. The reasoning is that it has a sidereal and geological similarity to Earth. So we can expect the resources to be abundant, and getting at them will be a similar experience to getting at them on Earth. The gravity is under half of that of Earth which means the accessibility is pretty good. The radiation protection requirements places all infrastructure for living and industry underground. The weak gravity also means that having offspring there may be impossible.
Score: 2 Res, 2 Acc, 1 Rad, 1 Gra +1 Zero-G Bonus = 7.
The near Earth asteroids, the moons of Mars and the asteroid belt are the most abundant resources in the inner solar system. Getting to them and moving between them is the easiest, in terms of energy, of all the alternatives. Radiation protection is available simply by digging into them which, considering the average density of most the asteroids we know about, could be done by robotic precursor missions or even by hand if necessary. Using rotating habitat structures, or even just a simple train driving around an endless loop of track, a full artificial gravity can be provided to the colonists. The easy access to zero gravity is also a bonus to industry.
The question of how much gravity humans need to produce healthy offspring must be answered before we can seriously discuss the colonization of the solar system. If it turns out that we need a full Earth gravity then it really does rule out most destinations until some future technology is developed to overcome it. To my mind, this question should be the primary focus of human adaptability experiments on the ISS and elsewhere in space. For example, a new short arm centrifuge module should be under production to be used for full gestation small mammal testing. Beyond the ISS, the planned robotic lunar landers should carry microarray experiments to test the affect of reduced gravity on human cells. If the expressed protein sequences are sufficiently similar to terrestrial control results then we can say with some confidence that reduced gravity is worth future study - such as landing a full gestation mammal testing module on the Moon.
Special thanks to Dr Jim Logan for inspiring the scoring system.