We chose Cayuga State Park as our base camp for a recent camping and wine tour. Very close to lots of wineries, Seneca Falls, the Montezuma Wildlife Preserve (highly recommended) and if you like shopping, the Waterloo Outlets. Sampson would be a second choice in that area.
There are many great DEC campgrounds in the Adirondacks Park to consider. Our favorite is Fish Creek and Rollins which offer the ideal lakeside camping experience, but there are others we like as well.
Do visit the ADK Museum in Blue Mountain, the Wild Center in Tupper Lake, Whiteface Mountain. Also recommend the boat tour of Lake Placid. Lake Placid (the lake) is pretty spectacular. Lots of other things to do in Lake Placid.
If you camp at any of the DEC or NY State campgrounds, I have over 20,000 photos of each individual campsites at most of the Adirondack campgrounds available at http://campadk.com/campsitephotos.html .
If you must have hookups, then I'd suggest the KOA in Wilmington near Whiteface when you are in the area to visit Lake Placid.