Syracuse NY April Camping

I'm from Long Island and I was able to get a COVID vaccine appointment at the Syracuse Fairgrounds in April. Are there any campgrounds open then? I looked at a few but the ones I looked at open May 1. Just looking at a Friday checkin and Sunday checkout. It's 6 hours one way and I don't feel like doing a round trip of 12+ hours with a 9 month old. :-)

Thanks!