Pizza is very controversial in Boston. Frankly, I think it's all mediocre compared w/ other cities, but I do like a newish local chain called Upper Crust.
Tons of seafood, of course. Honestly, I prefer the chain McCormick & Schmick to any of the local stuff. But if you like 150-year old ambiance, Union Oyster House is solid. And it's said of Durgin Park by Quincy Market that the Kennedy boys ate there when they were young, and the same waitresses still work there.
Museum of Science is a matter of taste.
Museum of Fine Arts isn't up with the greatest-greats of the world (e.g., Metropolitan in NYC), but is very well worth stopping in.
Best Revolutionary War place to go is Concord, but that requires a car. The Freedom Trail ties together a number of minor venues well.
Harvard's Museum of Natural History has some very cool stuff, including a rock/mineral collection I've seen surpassed only one other place (but that one, American Museum of Natural History in NY, blows it all to hell). Plus lotsa skeletons and the famed glass flowers. Getting to Harvard from downtown is NOT hard -- take the Red Line from Park Street. As with all major universities, if you did try to take car to it parking would be an issue anyway.
The JFK Museum is more building than exhibits, but still has some good stuff. I forget whether it has a subway stop or not; it would be pretty nuts not to. (It was originally to be built at Harvard, but the City of Cambridge rejected it due to traffic/parking issues ...
Newbury Street in the Back Bay is the art gallery "shopping" street.
If you happen to like classical music, Symphony Hall (Boston), Jordan Hall (ditto), and Sanders Theatre (Harvard) are three of the best venues I know anywhere. But the summer program is obviously hit-or-miss.
I now prefer to see my wild animals in the wild, including aquatic ones. But the Aquarium is indeed a good one as those things go.
