Choosing camp isn't a terribly linear endeavor; it's more of a matrix of cost, goals, and needs. I firmly believe that the place to start is with the cost. Don't research the ideal camp, get all excited about it, and then discover you need to take out a second mortgage to afford it.
Remember to consider all the factors likely to draw dollahs from your wallet-- basic tuition, room and board, travel, spending money, extra coaching, uniforms, books or equipment, etc. Some camps have a basic package, and then charge extra for specialty classes, private lessons, celebrity guest coaches, etc.
Know what type of skater you have (and be honest with yourself)
National trajectory? (Novice test and triple jumps at age 12 or so); strong recreational skater (planning to test through Senior by end of high school, does some competitions); competitive (planning to test through Senior, goes to qualifying competitions); recreational skater (favorite activity is the ice show, but still committed to testing and improving); social skater ("what's testing?").
That said, a good summer program has the ability to move your skater onto a different track-- from strong recreational, for instance, to competitive, or competitive to national ambitions.
How much skating will my kid put up with
A recreational, half-day program is going to have an hour and a half of ice in two 45-minute sessions. Skating this much every day is going to result in improvement, but it's not going to get you to nationals. On the other hand, a more high-powered program with 4 to 6 hours of ice and off-ice training every day is not going to be a fit for someone who's in it for the social scene.
Who is coaching
Don't be dazzled by a name, nor dismiss the unknown coach. Check out who their students are. A coach with multiple competitors and zero recreational skaters is not going to be a good fit for your recreational skaters. (Many highly competitive coaches also teach tot classes; I'm not saying competitive coaches are terrible recreational coaches, but that coaches who don't like to teach recreational skaters are not going to be good with a recreational skater just because it's your kid.)
Find the coach who teaches kids like yours, or like the skater your kid wants to be.
Conversely, a coach who has never had competitive success is unlikely to start with your kid. Doesn't have to be Frank Carroll, but some competitive record is a good indicator. (For the most part. All coaches have to start somewhere.) And camps are a great place to network-- both for your skater and your regular coach to start making those very important connections.
Camps will publish bios of their faculty, generally on the website, but read between the lines. A coach who has really had international competitors will generally specific at least the competition, if not the name of the skater or skaters. Professional Skaters Association rankings are another good indicator of how honest a bio is. If the coach is claiming multiple high powered competitors but not noting their PSA ranking (not the same as rating), take the bio with a grain of salt.
Who goes (or has gone) to this camp?
Check your goals-- national competition? Senior test? Pizza night?-- and see which program has students that share them. Programs that have famous "graduates" will promote this. I would rely less on endorsements, as those can be, literally, bought.