Harvard Square, North End, etc.
Take the T red line to Harvard Square and see the sights, and of course the Harvard campus itself. The Longfellow House is walking distance from campus, which is pretty good if you have the time.
One night for dinner go to the North End, which is the Little Italy of Boston. It has fantastic restaurants and bakeries, and just really neat to walk around. The Old North Church is there (“one if by land, two if by sea”).
Like everyone says, the Freedom Trail is the best way to capture the cities history, and the USS Constitution is a must. There should be free pamphlets which describes each site.
When we go we generally don't get a car in Boston, because the T (subway) is fantastic and you have to pay to park your car anywhere. But if you are looking for foliage, you may have to drive to catch the peak, maybe into New Hampshire. Thats a great trip in itself though. So after a few days in Boston we get a car and head out. Another great place, close by, is Concord. The Colonial Inn is really cool, and the Colonists hid munitions there. See the North Bridge, where the first British were killed, and the home of Louisa May Alcott, where she wrote Little Women. Plus walk some of the trail where the British fought their way back to Boston.
The Boston Museum of science is impressive, good for a rainy day. The Museum of Fine Arts is really good.
Some of the best clam chowder and crab cakes are at Legal's seafood in Cambridge.