I know he likes music, does he dance? Does he get embarrassed to dance with his mom? We do that if we're feeling cooped up sometimes... crank up music and dance like crazy for a while.
Bake -- it's a nice warm activity and you get goodies at the end of it too. If it's specifically a boredom-buster, making messes can be a good part of it (as long as the mess-maker helps with clean-up). I mean like rolling out dough, smooshing it up, cutting out shapes, that sort of thing.
Obvious -- books, TV, videogames. All more interesting if done in pairs, with commentary.
There must be kids in the vicinity, walking distance? Playdates are good (adults can only do so much for 7-year-olds....)
About to head out, will keep thinking....