"Where do we put the people" was asked
If you reach a level of science that allows such as I described above, (Most specifically high nanotech) then space is a trivial issue. High nanotech allows for massive solar power farming and thus massive energy availibility. This allows cheep space launch via electric rail launch. This allows for easy explotation of space, and construction of viable orbital habitats. (or moon or mars based teraforming)
Take a small asteroid. Drop it into a nice orbit, then unfurl some monofilm mirrors around it. Spin the rock as it heats, and it will spin up into a nice large hollow sphere (perhaps you help it ballon out with a low yeild fission charge, but it would be simpler to did it a few other ways). Let it cool. Spin it up to one G. Pop a hole in it. Use your nanotech to teraform the inside surface to nice soil and add structural features for reinforcement, drag over some cometary ice for water, and atmosphere (O2 and H cracked by nano again and recombined into CO2 also) and you have a dyson sphere able to comfortably house a few million folks. repeat as needed.
There are terrestial solutions also.
If you have a science that lets you do molecular repair of cells, you have a technology that can do some impressive feats of constuction. You can build just about anything anyplace, and have options for collecting huge amounts of power (Picture a few square miles of photovoltaic solar cells grown in the desert out of the sand and some seeded bots) cheep power lets you do even more...
Myriads