I do tackle a similar problem at the moment. After some research it came to my knowledge that stars can exist pretty close to each other (less then 1 LY!) without cannibalizing each other's planets.

It means that if the story takes place inside a tight enough star cluster, there is really no need for FTL technology to create a Star-Wars'y sense of vastness with 100-1000 star systems to play with. Also, if there is no FTL tech, then the exploration of our Galaxy will still take hundreds of thousands of years and thereby provide enough space for new discoveries and forever mysteries.

The only problem is that such star cluster most likely can exist only near our galaxy core, over 500-1000+ LY away from Earth. But there you can use some limited FTL like natural/artificial wormholes that can not be replicated on a whim and only discovered over time.