Arkansas has a number of nice state parks for all types of camping. I know you said not a state park, but many have trails like your asking about.
Map of Arkansas ? Arkansas map ? Arkansas state map
Have heard good reviews on a number of them, we have been to Lake Oachita near Hot Springs, and your correct lots of hills and water. But it does take time to get there There is a thread running elsewhere with pictures. This weekend (memorial day) the entire state was to get lots or rain, so when you call to reserve ask how wet the area is.
Much closer and a real nice park is Daingerfield SP
see this link and scrool and look for the pictures link. The lake is nice, you can hike around it, lots of shade
Daingerfield SP (July 2008)
Also consider Ft. Parker SP (hiking,swim and fish), Cooper Lake (Same) and even Inks is great for a good time.