If we manage to harness fusion power generation, bascially any spot in space could be made livable. If it turns out that the only fusion reactors that produce power start at a signficant fraction of a solar mass, even colonizing Mars will probably be out of the picture.
What other technological advances would we need? I can think of areas like manufacturing (how small can we make a "factory" that can act as the seed for the industrial infrastructury of a colony, i.e. it must be able to make copies of itself and manufacture useful stuff), molecular manufacturing (can we build a device that, given the description of a chemical, can assemble useful amounts of it from simpler molecules plus energy?), agriculture (can we come up with an ecosystem that's simple enough to work outside earth, but produces most of what the colonists need?), space propulsion, space launch technology (we need to come up with something better than chemical rockets at least for the first 100 miles of the trip), medicine (especially dealing with cancer, which will become a major problem when staying off Earth), etc.