Hey Marissa,
SPAM just got recognized for their camp in a box summer camp curriculum. Their
website has information on how to put one together, and you can also contact them through the website. I left the team when the program was in it's infant stages, and the kids seemed to have fun.
The timeline document says you need about a pound of lego per student. That was the closest to a price estimate I could find. Also as Arhowk mentioned, the price will vary dramatically depending on the type of camp you had in mind.