Jo - it's hard to go wrong with any of the Georgia State Parks. I have not been to Reed Bingham, but have stayed at FDR many times.
Be advised that the 3 mile trip from Hwy 27 across GA 190 to the park office is a climb the whole way, but not a difficult one. Once you check in at the office, the road to the CG is a fairly steep downhill grade. I didn't find it a problem, the road is wide and the curves are gentle, but some people don't like it.
That being said, once you are checked in, there is a "back entrance" to the CG that is flat and level and the quickest way to get to the town of Pine Mountain. Unfortunately, they aren't set up to let you come in that entrance to check in - you have to go to the park office first.
The campsites are all nice and level and most of them should be able to handle your rig. There are some pull thrus and some back ins that are right on the lake. The bath houses are older, but always clean.
While in the area, Pine Mountain is great for antique fans and Callaway Gardens is a must see for the nature lovers. Take your bikes to Callaway, they have miles of paved bike paths thru the park.