Fanueil Hall - ditto. Us locals call it Quincy Market and that is pronounced as Quinzee Mahket. Don't call it Quin-see.
Regina's Pizza - ditto. In the North End and they also have a place in Quincy Market. Never been to the Polcari's Italian restaurant in Maine (same family). I'm sure it's great but why you would drive to Maine for Italian when you have the North End right there? Maybe it's really great, I don't know. Maybe you want to see Maine. When I think of Maine I think of lobster (e.g. Barnacle Billy's:
http://www.barnbilly.com/). If you want to drive to get Italian, Providence is a terrific destination.
Armando's in Cambridge is my favorite pizza, if you are in that area. It's off the beaten path and if you don't want to go to a great deal of adventure to get a slice, Regina's will certainly do.
If you're looking for a hole in the wall/no frills place with fresh seafood, Belle Isle near the airport is where I get crab rolls and lobster rolls. if you must have it fried, clam rolls are good, too.
http://belleisleseafood.com/ Cash only, and I would be shocked if you ran into any non-locals.
Hilltop?? Really? It is an icon definitely, but I don't remember it being very good. But I haven't been there since I was a kid so I could be way off. They were always known for the big fiberglass cows out front. Some MIT students stole one a few years back and put it on the roof of a building on campus.
My favorite places in general are Coolidge Corner (on the green line in Brookline - there's a great independent bookstore with lots of author readings and an arthouse movie theater across the street; Tons of places to eat and entertain yourself) and Harvard Square (on the red line in Cambridge, must-see).
There's a Chinatown and lots of ethnic places all over town. Somewhat near Fenway Park at the St. Mary's stop (Green Line), you will find a French/Cambodian place called Elephant Walk
http://www.elephantwalk.com/ where we've taken my mom for Mother's Day Brunch the past couple years. This is the only place I've mentioned that isn't what you'd describe as super-affordable. but certainly reasonable.
Embrace the T, bring walking shoes, and whatever you do, avoid the Cheers tourist trap. And don't you dare wear a Yankees hat. We'll tolerate New Yorkers but don't push your luck.
-Mike
former Legal Seafoods busboy, circa 1988
