As an official Band Geek Mom, I'm providing some local camp recommendations for parents of music-loving kids who are old enough for sleepaway camp.
Cazadero is a sleepaway camp for young musicians in Sonoma County, outside Guerneville near the Russian River. It's a gorgeous setting with a range of traditional camp activities and a focus on orchestra, band and jazz band. There's a range of camps for different ages, including a family camp, shorter camps for younger kids, and 12-day camps for middle- and high-schoolers. All students do orchestra and/or band, with jazz band as an adjunct. There's also piano and classical guitar.
For jazz-playing teens:
Stanford Jazz Workshop (residence or commuter)
Jazz Camp West -- this is really an adult camp that accepts older teens. (It doesn't have the youth-oriented structured activities that a teen camp would, and if you're not confident that your kid will behave, this is not the place.) It's my son's favorite place on Earth. It's just one week a year, in June, located at the Stonestown Y's Camp Jones Gulch in Pescadero. I showed up to pick up my son last year and he was jamming with a guy I'd gone to high school with, and also with venerable radio personality Mal Sharpe (who's a demon trombonist). They have vocal and jazz dance too.
Jazz Camp West's sponsor is now running a camp for musicians 10-14, too, which we haven't experienced ourselves: Jam Camp West.