At the current time, we are no where near colonizing on any cosmic body. The only two that would be even close to being capable of human habitation that we could reach in a relatively short period of time given our current abilities and technologies would be the moon and Mars.
While there is evidence that there is water in the moon which could be tapped, provided it really is there, to provide for a habitat of some kind. But habitation would most likely be nothing more than a base of some type instead of any kind of actual colonization. Since there is absolutely no atmosphere there, it would be impractical for anything other than more than a few dozen people, if that many. Constructing a base that could house and provide for more than that at a time is a rather tall order.
Mars, on the other hand, is different. Currently, more than a base or two there is also impractical. The gravity is about 38% that of Earth, so that is something any human occupants will have to deal with. Indications are that water was at one time abundant on Mars, and it thought that there could be a large reservoir of water underground. If found, that could be a huge building block for a base. While it is more Earth-like than the moon, the atmosphere is extremely thin and unbreathable. It is made up primarily of carbon dioxide (95%.) But it is the make-up of the atmosphere that makes some scientists believe that it would be possible to terra-form Mars that would make it look like Earth and make the atmosphere breathable.
Here's an article on how that could be done.
But don't start putting money aside for a ticket to Mars just yet. Even if hey were to begin the process within the next few years, it would that several hundred, if not thousands, of years to accomplish. Anyplace beyond Mars is simply too cold to even consider attempting to send humans to. Some might say the Saturnian moon Titan since it is thought to be like early earth, it is unlikely we could ever warm it up enough and transform the atmosphere to a breathable air (it is made up primarily of methane.)
As for going beyond our own solar system, even to the nearest star system, it would probably be faster to terra-form Mars than it would to develop the technology to do that. We are nowhere near as far along as the chart askold posted above.