My kids started going after 8th grade. One was newly 14, the other is very young for her year, so still 13. Both did absolutely fine.
The 11-15yo age group is particularly hard for camp. Almost all the programs are geared toward orchestra and very few are serious. Even Interlochen at this age is not particularly high level. Only the oldest division, which starts with sophomores, is considered high level.
Of the programs I listed above, Kinhaven and Greenwood typically place a 13yo in junior division. Junior division is way less serious and level is lower, especially for Kinhaven.
Ascent is officially 14+ but allowed 13yo to apply this year. The kids I know who went were more 15+. This program is new, so I don’t know much about it.
Encore is mostly older kids, though it is officially 13-25. The people I know there were all 15+.
Meadowmount is 13+ and there are usually at least a handful of kids in that age group there.
Center Stage Strings is 12+ and there are always quite a number of 12-14yo. The younger kids are typically very high level.
Heifetz is now putting almost everyone under 15 into the junior program. That program this year was ages 7-15, so quite a spread. There were definitely more kids in the 13-15yo range there this year then in the past. However, I’ve also heard a lot of people complain about the curriculum in the junior program, with the kids not having enough structured activity. Not speaking from experience, though, just reporting. It’s definitely different in character from the senior program.
Morningside and Perlman are both 12+. Everybody is good and serious.
NYO2 and BUTI are 14+. NYO2 has a very definitive age cutoff. BUTI will consider younger kids if and only if there are extra spots open.
I forgot to mention Bowdoin – great program for late high school or college, but I don’t like it for younger kids as it has zero structure.