Assuming you want full service the one's I have used are the former KOA in Old Forge, Thornbush Acres in Indian Lake, and the KOA in Lake George.
https://www.oldforgecamping.com/
Thornbush Acres
There are a few more but I have not stayed in them. There are many state campgrounds but few have anything other than space. There is a strip along I-86 that is loaded but more party city than wilderness experience. There is also a KOA North of Placid.
FWIW I would stay a week or two at a time in several different places. There is a difference in flavor as one moves around. Also do the Adirondack Museum in Blue Mountain Lake and the Natural History Museum in Tupper. Different and superb. ;-)