Stagedoor Manor had a limited number of openings for Sessions 1 and 3 last year that didn’t close until very late. It might be worth looking at to see if that is the case again this year. French Woods nearby may have openings as well.
No audition required to get into the camp, but there are a lot of talented kids there. You might want to check into it. My daughter had a lot of fun there last summer, but we felt it was a bit pricey for only 3 weeks. And, for visiting parents coming to see the shows the final weekend, the area is VERY rural and a complete 180 from NYC.