Last week we camped on the island in Lake Santeetlah. It's a great spot for taking the dogs, as we don't have to worry that they will disappear into the woods after a raccoon. In the map below, you can see the island near the middle of the map. We put in a the Santeetlah Marina, and it's a five minute pontoon ride. We have also camped near the island and paddled our canoe from the Marina. It's very doable if you don't mind to paddle for a nice spot.
If you don't have a boat, you can rent one at the Santeetlah Marina. Also, there are lakefront sites that do not require a boat. Look at the top of the map and you'll see campsites scattered along the roadside. If you like creekside instead, check out Horse Cove and Rattler Ford. You'll find a little bit of info about those campgrounds here.