Dupnisa Cave is the headline excursion from Kırklareli. The cave system runs through the Strandzha hills and has show sections with stalactites, stalagmites, cool air, and an underground stream.
It takes effort to reach without a car, but it is the one sight in the area that feels like a clear day-trip reward. Combine it with a drive through the forests if you are using Kırklareli as a base.