I have to disagree with the above posters. Melting pot is neither budget friendly or family friendly, I consider it more an adults night out or a romantic dinner.
I would highly recommend something in the North End for Dinner (Hanover Street), but alot of them are cash only so be prepared for that. Also get there on the earlier side as the restaurants are small, but you won't get a better Italian meal and I would be surprised if you were disappointed.
I disagree completely about Durgin Park, I have not been there lately, but I was NOT impressed the last time and think it's much more touristy than what the locals would do.
Cheer's again, you are going there for name only, food is nothing outstanding.
Since you will be near the aquarium there are several good fish restaurants in that area, One especially, named - no name fish restaurant.
Quincy Market is fun, but expensive some of the outside restaurants are better.