>Wormholes: Just bend the fabric of reality over on itself like a piece of paper. There's even some talk that such a thing might even be possible, though it's still in the realm of science fiction.

>Dimensional shift: Another version of FTL travel is to phase through dimensions, which are all expanding and rotating at different speeds. You might not be where you want in this world, but you and your crew can swap places with other versions of yourself with ones that are. And because there are an infinite number of parallel dimensions, you can find one that's near identical to this one save for your ship being closer to where you want to go. This can even host some hijinks when the computer screws up a calculation, and characters have radically different personalities or events have transpired after a FTL jump. The comic where this idea was originally used, the main character just used FTL one day and jumped to a world where his love interest was dead, and he's been trying to get back with her ever since.

>Anything else: Alien tech no one really understands, magic, teleportation, etc. 

LST or FTL travel is always going to require [i]some[/i] explanation so that it doesn't get abused, but there are a lot of ways you can do it. You just have to decide what works best for the narrative.