My kids went to where they are watched. I thought they might be too old since they are 9 and 12, but they knew that there were video games there. My son played video games and my daughter played with two girls that were a little younger than her. I had thought they would have liked to see the rooms too, but they said they would stay there. At 13 and 15 could they stroll around Saratoga Springs a little? You wouldn't be far from where the pool is and once we were leaving we noticed we were near the tennis courts also. We were going to walk around for a few minutes, but then the van was ready for us.
They have a nice play area where they will watch the kids for you. When we went (this was at Boardwalk) there were several other children there at the same time.
They do "take care of them" but your kids are liable to be VERY bored with the activities provided. (They tend to gear towards little kids LOL!) I would turn them lose in the closest arcade with a few bucks and a cell phone!