Caledonia State Park is very close to Falling Springs.
Pine Grove Furnace SP is closer to Breeches/Letort/Big Spring/Mountain Creek. Be aware that these parks are very popular and crowded on weekends in the summer, but I think their campsites are a bit less crowded. May want to give 'em a call to reserve a spot. There is also a private campground near PG called Mountain Creek Campground but I'm not sure they have tent sites.
Here in Gettysburg, we have a lot of campsites, but they are mostly for campers/RVs and the distance to the streams is further, about 40 min to Breeches and further for Letort or Big Spring.
If it were me, I'd definitely look into Pine Grove Furnace SP.