Not sure if these fit the criteria of being 20 minutes away.
Winnipesaukee Playhouse Summer Camp
NH Boat Museum Summer Events which include Youth Boat Building, Youth Sailing and a Family Boat Building Week.
There should be a few more camps to choose from in the Lake Links, here are a few to start with:
Camp Birchmont
Camp Bernadette
Camp Menotomy
Camp Quinebarge
Camp Wicosuta
Pleasant Valley