Coolidge Dam (which forms San Carlos Lake) is in a little traveled part of Arizona (East Southeast of Phoenix), and it's pretty neat to actually see real quantities of water surrounded by desert. There is a small campground, but overall the site seems little used by the public. The scenery is beautiful, and the dam was obviously built during the days when architectural style counted for something. It's worth a detour if you're in upper Arizona - it's on the way to Globe AZ (AZ 70 coming from Safford). Traveler's hint - enter Rt. 3 to the dam from the Peridot side (West), the other way (from Calva) is through an Indian reservation and the road, while passable, is not too much fun. The other way is an easy shot off the interstate.
If you like to fish but don't care for crowds, Coolidge Dam is definitely the place for you. There are several boat launch areas and several campsites, both primitive and some large enough for RVs.
Below is the view from a picnic site where I had lunch. Gorgeous view - nobody around, but I was there on a Monday - maybe it's busier on the weekend.