I came here to recommend Lake Owen in Wisconsin only to find out it closed nearly a decade ago! Can't believe it. I had a really good time at International Gymnastics Camp, but that's in Pennsylvania.
Most camps have a wide variety of skill levels, and when I was a kid, we just did an assessment the first day to determine groups.
My other suggestion would be to look at colleges, even outside of Division 1. My first ever sleep away gymnastics camp was at UW-Whitewater, and I had a ton of fun and learned a lot that really helped my gymnastics. We stayed in the dorms and it was a week long, with an option to do a weekend apparatus camp, and to stay a second week. I was training level 5 (age 7) the summer I went and there were a lot of girls above me and some below me as well. There weren't as many recreation options as you'll find at Woodward or IGC, but it was also less expensive, about an hour from home, and good introduction to camp at that age.