Harvard Square is a must, if anything for the people-watching and the ice cream (Toscanini's is the best). Some good, fun shopping there as well.
A tourist favorite is Faneuil Hall (on the Freedom Trail), which is a marketplace with tons of restaurants (Cheers, Salty Dog, Ned Devine's Irish Bar, etc.) and shops.
Another good people-watching place is Newberry Street, but not in the same way as Harvard Square. This is the upscale crowd here.
If you're into microbrews, IMO the Cambridge Brewing Co. (near MIT) has the best. Boston Beer Works (near Fenway) is OK. You might want to check out an Irish bar while you're here. There's nothing like drinking a Guinness at a bar while surrounded by Irish accents!
If you're looking for a good seafood place on the water, Anthony's Pier 4 has a great atmosphere. You can watch the boats in the harbor and also the planes take off and land at the airport. (Admittedly, the view is a bit better than the food, but it's still damn good seafood.) A local favorite is No Name on the fish pier, which is a hole in the wall, but great food! My favorite is still Legal Sea Food, which are located in several places in the city (and Cambridge).