D.B.
Cards, Uno, Mad Libs, puzzle books (variety puzzles are the best), a set of mechanical pencils so they are always sharp without a pencil sharpener), a frisbee, a yoyo (yes, kids still go for these old-style toys), some of those puzzles with interconnected rings or the simple wood puzzles with golf tees as markers (the kids can share - great for "down time"). Food is a problem in camps and usually isn't allowed - so it's good that you are avoiding it. Between food sensitivities and unwanted animals coming into bunks, it's a problem.
You could also put in some stationery, stamped envelopes (pre-addressed if you want to) and put in some conversation starters (even if you print it on the stationery) - the best thing about camp is…I wish you could see the….the funniest thing that happened this week is….my counselor's name is….etc.