We could do it right now. There just isn't enough money or anticipated benefit to science to justify it.Realistically, how many years are we away from colonizing:
The Moon
The moon is "easily" kept supplied from Earth compared to Mars. A Mars colony really sort of needs to be self-contained, self-reliant. This becomes MUCH easier when a reliable source of water can be identified. Assuming that can be found, and again that the money and/or scientific benefit limitations are also overcome, I'd say 20 years (?) from today before plans could be finalized and committed to, then another 20 before it's actually on its feet.Mars
Absolutely indeterminate. Short of purely fictional science and Star Trek levels of global peace and prosperity for the project, interstellar distances are functionally impractical for humanity to bridge with a colonization effort. It's strictly a theoretical possibility. May as well pick a date out of a hat - and then the technology available will likely make current technology seem literally stone-age.Any planet outside the Solar System
Realistically is the key problem here.Realistically, how many years are we away from colonizing:
As the Man pointed out, the trick is motivation.We could do it right now. There just isn't enough money or anticipated benefit to science to justify it.
I don't think we'll ever colonize the Moon. There will never be a reason for it. There's stuff we could mine, like Helium 3 (if it's actually abundant there, and if we can ever actually get fusion to work so we can use it for it), but we don't need to colonize it for that. Robots controlled from orbit, or better yet Earth, are more likely....My guess: 30 years, minimum, for the Moon...
We have the technology. We could do it tomorrow.
Nuclear torch rockets easily get all the mass of all the equipment we'd need into orbit, and to other planets.
Protection against radiation and micrometeorites is easy if you have a big enough mass of materials to build a properly shielded ship.
I don't think we'll ever colonize the Moon. There will never be a reason for it.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.