I’d recommend the Isabella Stuart Gardner Museum. It’s right near the Museum of Fine Arts, but much less expensive (I think only $3-$5? with some days free). It’s a beautiful museum, and won’t take much of your time, either.
Also, as far as restaurants go, it really depends on your taste. Want some abuse? Dick’s Last Resort, at the Prudential. The waiters are basically paid to be asses, and the food’s pretty good. It’s kind of pricey for what it is, but it’s fun if that’s your thing.
If you want to spend a lot of money on dinner, I’d recommend Morton’s Steak House . I dont know your financial situation, though, so be warned that dinner for two, including a bottle of wine and tip, ends up at about $200. I went there w/ my fiance, as we got a gift certificate from my parents for $100 as an engagement present. Best. Steak. Ever. if you have the means, which I probably won’t for a long, long time.
I’ll second Boston Beer Works, the beer is good and so is the food. If the weather is crappy, avoid Fanuiel Hall, as you’ll be outside a lot of the time. Newbury Street is good for shopping, they have both high end and lower end stores, so whatever your tastes you’ll probably find something you like. Right in that area is also the Prudential and Copley, both of which have a lot of stores, though Copley tends to the more high-end stuff.
If you DO decide to go to the Science Museum (I had a ball the last time I went), be forewarned that the train doesn’t run all the way there due to construction. There is a shuttle bus (that you don’t have to pay extra for) that goes from Gov’t Center to Lechemere, but it takes a little longer. I’ve seen a lot of tourists get really confused when the T driver announces the last stop, when the T map says it goes all the way to Lechemere.
Since you’ll be by the medical centers, there are a few places around there to go, also. The Linwood Bar and Grill is great. They have a good variety of food, and were featured on the Phantom Gourmet. Prices aren’t bad.
Also there is Thornton’s (not to be confused w/ the Thornton’s on Mass. Ave, totally different places). It’s more of a diner, and I used to live right around the block from there and ate there all the time. Good food, cheap, and they serve breakfast until 2 or 3pm on weekends.