Lets survive the next few hundred years a species first, eh? We have a long way to go to make that happen, and a big part of it definitely involves mastering travel around and mining of our solar system. It probably doesn't involve the expense and resources of major colonization efforts though, barring truly enormous breakthroughs in materials science, energy production and storage.

Lets focus on that, since without those factors a billion years will just find the raccoons or squid that replaced us facing the same problem.