Breakfast -
Omni Parker House on School Street. Do not miss it. It's classy, so you'll want to wear a least a polo shirt and closed toe shoes, even for breakfast. It's expensive for breakfast but worth it for the history and the quality of food and history. (Its like $15-$20 per plate)

Seafood -
"No Name" on Fish Pier. Historical, but not the best seafood.
"Strega" North End or Waterfront - two locations. Great food. Will cost you a lot, but worth it. Make Reservations. I'd recommend North End. --- this is Italian Seafood. Don't go expecting fried scallops. (Caution expect $40/plate)

China Town (brunch) -
Chou Chou City for Dim Sum in Chinatown. It's fun. Not your stereotypical Boston. (Its Dim Sum, not seafood).