Take the Chinatown bus to NYC and show them a real city
Just kidding. But yeah, I agree that you shouldn't have to take them away from the city to have a good time. Definitely hit some seafood, but I'd say you might as well pay the extra to go to Legal Seafood, just because it's the thing to do if you're visiting Boston. No need to skimp there. Plus, their clam chowder is insanely good.
Maybe some shopping on Newbury, a walk through Boston Common, the witch museum in Salem. Plenty of other museums, if they're into that.
But, touristy stuff aside, show them the stuff you enjoy; I'm sure that's what will appeal to them most. I'm not sure what is available to under 21s besides Centerfolds
, but I've been to Ohio and the nightlife in Boston is going to be a helluva a lot more interesting than the nightlife in Cincy, Cleveland, or wherever.