I recently read the Bobiverse where they don't have FTL travel at all. They have a reactionless drive that pushes against subspace and allows accelerations to be limited by G-forces instead of fuel limits. So a ship running on AI with its passengers in cryosleep can spend ten years going to a new star system BUT because its managed to accelerate so fast the AI only experienced 5 years due to time dilation. It made for an interesting setting needing to account for a decades long trip between star systems even after FTL communication was invented.

And I like The Mote In God's Eye where they have instantaneous travel between jump points that connect pairs of stars but only between those jump points. Regular travel within a system is still using fusion engines and reaction mass.

There's a line in Star Trek that is mentioned once as a basic rule that everyone knows then never brought up again "When faster than light, no left or right" that is, warp travel must be in a straight line. So I thought about a system where you need to use a star as a metaphorical springboard to launch off into interstellar space and you can maintain your FTL speed but can't change direction. And if you have to drop out of FTL you're now stuck in interstellar space decades from rescue.

I like the idea of a star being the interstellar travel hub of a system. Perhaps a swarm of jump gates around the star that mumble mumble gravity folding space mumble mumble use the star to create the FTL jump towards the target star. So to go to Alpha Centauri you need to position yourself on the opposite side of Sol and dive into the star before the FTL drive activates. It would make the star a bustling hub of activity with all the ships arriving and leaving before going to/from the planets further out.

Can anyone cite any other unique approaches to FTL beyond the standard "Set destination, press Engage, ship go fast now"