Need a great vacation spot with theme park for 3 & 4 yr old. I live in NY?

We are from Ny. Looking to travel first week in June and wanting to stay within 6 hours of our home (long island). We are looking for a theme park just for kids. We were going to go to Story Land in NH, but I’m afraid the weather might be too cold. I dont mind going south bc it will be warmer but I can’t find anything. Any suggestions? thanks