Even if you manage to create a self-sustaining space station, that's going to cap the number of viable residents pretty low unless it's truly massive. And I don't even want to think about the psychological toll of being one of the last few dozen humans orbiting a dead Earth.

Tangent: Seveneves by Neal Stephenson is a hard sci-fi novel that explores this very situation.

Present day humanity (i.e., no manned interplanetary missions, minimal manned presence in orbit, etc.) discovers total-extinction cataclysm will happen in two years. Scramble to figure out short (how to get genetically viable population into orbit) and long (how to keep them alive for a thousand years until the surface is habitable again) term solutions to preserve humanity.

True. Doesn't make any sense sending things down a gravity well. Unless of course the resources to be mined are too valuable down there.