I think it would be neat to add a mechanic to multi-star systems, that if you have arrived inside one of the stars via FTL, that it teleports you safely to a random nearby non-star sector, with a high velocity away from the star in the same direction as the random non-star sector from the original arrival sector, to simulate a gravity slingshot. This might be a good alternative to FTL arrival in a regular single-star sector as well.
(But please, no time-travel to 1980's San Francisco.)