When I was a kid I only attended summer camp twice. The one time was for a week at Mt. Tremper while Dad was the chaplain for that week. I recall my brother and I got to stay in the cabins, but my sister was too young and stayed in the big house with mom and dad.
The only other camp was a month at Farm Camp Lowy. This was in 1969, the year they walked on the moon. This was while we were living in Brooklyn, and Mom was doing her babysitting thing. One of the parents had just taken over this camp and offered a deal for both my brother and I to go. It was for a month and was up near Deposit, New York as I recall. They had a lake and I learned how to sail using the Sailfish they had.
One time I was out on the lake with my brother and I sailed all the way up to the other end of the lake. This lake as I recall was surrounded by mountains. I think I sort of ran into a dead zone, as once I was in this end of the lake I could not catch any wind. They had to come out in the motor boat and tow us back. My brother had to lie across the front of the boat holding the tow rope while I was in the back with the tiller. He never let me forget how I got us stuck.
I wonder if the camp is still in existence. They only had two month long session. We had gone up in July. I fell "deeply" in love and demanded that my parents let me stay another month. That would have been the family vacation month.
Needless to say I did not get to stay, and who knows what happened to that crush? I seem to recall they had an annual reunion each fall in a hotel meeting room to allow all the kids to get together and bring each other up to date.
As far as the specialty camps, except in the case of a prodigy, I would think an ideal camp would be one that still has a number of different activities to entertain. To specialize at this point except if it was to bring a child up to speed, weight reduction, or remedial education for example, the ideal camp would allow your child to get to interact with peers that are into different activities and be able to try new things.
Hanging out with all computer nerds, for a few weeks, to the exclusion of meeting kids that like to paint, swim, boating, water skiing, mountain bike, etc., makes no sense to me. While your child might think he loves the theatre, it would certainly be better to let him spend a portion of the summer still learning about other skills and hobbies in an environment that is also filled with new kids to really help sharpen his people skills.
Just some ideas to keep in mind. While I agree it is better to be a master of a few trades than a jack of all, I do think limiting a child's exposure to all that life has to offer is not good for the child in the long run.