Boston is quite possibly the best city to visit in our country. It's clean, safe, walkable, and there is a ton to do.
Like others have said, the Freedom Trail is great. We like the North End. Eat some Italian. One we like to go to is called Trattoria Il Panino. After you eat you can get a dessert at Mikes Pastry or Modern and just walk around. You'll probably run into some history.
Best lobster roll: Tie between Neptune Oyster in North End (small, you'll likely wait) and Salty Girl near Copley Square. Get them warm with butter rather than cold with mayo. Honorable mention - James Hook & Co.
Higher end shopping is in Back Bay, Newberry St. and Copley Plaza.
The T (subway) is great for getting around. It's cheap and much cleaner than New York.
Others have said go to Salem. We liked it. You can take the commuter train for like $8 from Boston Garden. Beautiful old houses, some haunted history. It's about a 30 minute train ride.