For a place very close to The Garden, I'd recommend Flat Iron. I think people 21-ish would enjoy the vibe, and the small plates concept. Plus, the food is quite good.
If they're in a more pizza and beer mood, I agree with winedude; Regina's. Although The Waterfront Cafe is also nearby and has pretty darn good food too (including pizza).
Agreed. My top choices by the Garden are:
(1) the North End - Ernesto's for a slice, Regina's for a pie, or Pomodoro for what remains by far my favorite fried calamari with my favorite marinara and either chicken and ziti carbonara or chicken marsala, or
(2) Flat Iron - hip, tasty, small plates with nice cocktails about 2 blocks from the Garden.