There are 3 in Watkins Glen. We've stayed at the KOA and Clute Park. If you do the KOA, try to get a site in the outback. Nicer sites, less noise. The KOA is close to the raceway; be sure to check the racing schedule.
Clute was fine but tight. Walmart next door, within walking distance of downtown. Speaking of downtown, there's a state park there. We haven't stayed there but it gets good
reviews 30 amp electric only.
As far as the wineries, there are a lot. You could do the west side of the lake one day and the east side on a second. A visit to the flea market in Penn Yan is worth the trip. I think it's only open on Saturdays.
I second Bob's recommendation. We did both sides in one day and by time we got half way through the tastings were taking their toll. Good thing my brother was driving.