As mentioned earlier The KOA at watkins Glen, FHU sites in the back part of the campground are large, newer but more $$. The below pic is the newer back part of the KOA. We wanted to keep our cost down so we stayed up towards the entrance.
Though we didn't stay over night at Clute Park, we did take a drive through the place and checked on a few things. We would stay there also though thought the bathrooms/showers were clean but were in need of updating. Probable not an issue for you but was more for us.
Excellent craft beer in the area, check out the beer trail also! :C
Mike