It is the year 2500. The solar system is teeming with colonies, from terraformed Mars to the cloud cities of Venus to the asteroid mining colonies and beyond. It is all possible due to the Thread Network of superdense filaments linking colonies in an ever expanding transit system wen. But suddenly, the Lucust Fleet arrives, attacking humanity (including augmented humans, uplifted animals, sentient machines and other transhuman beings) and nearly causing our extinction. Only a terrible gambit that causes a massive solar storm defeats the Locust Fleet, but at a unimaginable cost. Most of the utopian technology of the solar civilization is destroyed. Between that and the depradations of the Locust Fleet, the solar system is a post apocalyptic hellscape. The Thread Network remains, however, since it is built on a function of physics, not technology. Anyone who can jury rig a space worthy rocket plane into space can traverse the colonies. But who knows what they will find in the ruins?
See? Straight up post apocalyptic setting with space travel not just possible but a central conceit.