I like the Aurora idea; even more than Voyager, you could see how FED citizens react to non-FED situations: Do they hold fast to the PD, at the risk of making enemies of the new locals and/or running out of resources? Depending on their new situation they might even need to hide themselves from said locals, to avoid being attacked.
A neat series hook would be an older model ship, used for something mundane (transport, system defense, or maybe even a training ship) pressed back into service to support this lost colony. It's crew a mix of SF officers and civillian specialists trying to figure out what's happened, search for materials to help run the colony and check up on the locals.
As for an enemy in this new region, you could go several ways: DQ style fragmented territory with no real major powers, a TOS with a couple of major powers and some smaller ones vieing for favor, or have one monolitic culture that holds sway over everything in the area (this would be bad for new arrivals...).
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"Yes, it's the Apocalypse alright. I always thought I'd have a hand in it"
Professor Farnsworth