"It doesn't change the fact however, that space is really, really big, and it would certainly take decades - if not centuries - to do 8 light years to our next nearest star"
It doesn't necessarily take that long for the crew. A constant 1g acceleration would get you to near c in 30 years; cruise for a bit with the engine off; then decelerate at 1g for 30 years. As time is hardly passing on board at all during the weightless period it is (a) not that uncomfortable and (b) you can travel almost as far as you want in a few hours.
So if we can crack the propulsion system, and the living and breeding in space problem, pretty much everywhere in the universe is only about 3 human generations away. Of course, the civilisation they've left behind might be long gone ...