We stayed at Arrowhead Marina and RV Park on a recent trip to Maine. It turned out to be one of our favorite stops. Here is the view from our campsite:
Put in Albany and then zoom out. You will see a lot of campgrounds all to the east and west of Albany at some distance. Some are our of NYS. There is nothing at all shown near Albany.
Maybe check out the Copake KOA or Thompson's Lake SP. Not sure if they are close enough for what you want. We don't camp much in that area, but we do like the Saratoga Springs area alot. Alpine Lake is our favorite.
Not a big gambler, but the horse track in August is always a great time - its got a lot more history and character than any other tracks.