You can fast travel to mission start locations, for energy credits.
Regarding more 'permanent' Transwarp unlocks, as you progress through Diplomatic ranks (Now only visible in the DOff panel, dunno why), you get Transwarp powers to K7, Starbase 39, DS9 and possibly one more but I forget.
At least it doesn't take as long to travel in STO as it does in Skyrim. I've heard rumours that when we do finally get "One sector space to rule them all" the size will be increased, however the speed may be ramped up to match. I'm in support of either, because it would mean bumping into less people, and right now warp speeds feel... slow (But better than before sector space was revamped).