This is a great idea.
There are so many summer camps, so it seems fitting that there would be more RPG camps as that is such an inspirational hobby.
I am very interested in the outcome of your experiment as it might be modeled or repeated.
On the other hand, I'll bet many local game stores may already have experience with running summer camps or groups for young people. In fact, a year or two ago, I recall seeing on their web site that
Dragon's Lair in Austin held week-long summer gaming and RPG camps. I never got around to investigating it further.
As for suggestions on what to include, I think some sort of
collaborative world building activity would be very engaging.
One time when I was young, I was involved in a sort of art activity where about five people had to draw and decorate an island on a huge sheet of white paper.
It was sort of a team building exercise to see how we would all approach it. The big decision we all made at first was whether we would divide the island up into one piece for each person or if we would freely share and contribute to the whole space.
I thought the latter method would be the most interesting and fun. However, the group chose the less risky first method of each person having their own plot exclusively for their artwork.
Of course, with RPGs, the world building extends into semantics and narratives over just visuals.