I towed a 7000 lb utility trailer for a buddy of mine last year from Syracuse to Tampa.
The South Carolina boarder is about 12 hours of diving. That was plenty while towing. If you want a hotel, avoid the "South of the Boarder" tourist trap. Go a bit further south
There is a Flying J on I95 at exit 181 just south of "Pedro".
Since we where towing a utility trailer we needed a hotel, so I can't help you with camp grounds.
Also, here are the Flying J fuel stops I made on the trip. I planned the trip with the assumption that I'd get 11mpg and I wanted a 8-10 gallon reserve. I also made sure that I took advantage of states with lower fuel taxes (VA, GA).
Desc. Miles Route Exit #
Home to Carlisle, PA 295 I-81 52
Carlisle, PA to Ruther Glen, VA 201 I-95 104
Ruther Glen, VA to Latta, SC 310 I-95 181
Latta, SC to Brunswick, GA 272 I-95 29
Brunswick, GA to Dade City, FL 238 I-75 285