Well, the first thing anyone is going to tell you is to see Faneuil Hall/Quincy Market. It has tons of shopping/restaurants and Quincy Market is right in the center offering a lot of food stands.
If you like history and that is what Boston is about, you should walk the Freedom Trail. You can see all the historic sites, including Paul Revere's House, the spot where the Boston Massacre began, the Old State House, grave of Samuel Adams, as well as Bunker Hill and the U.S.S. Constitition.
Fenway Park is awesome - if you go during baseball season - you have to see a game. It like watching old time baseball since the stadium is so small.
If you go in summer and you want a day to relax - I would recommend taking a walk on the Esplanade (right on the Charles River)
If you have time to venture out of Boston, I would recommend going to Marblehead (beautiful town on the water - cute shops and great place to have lunch.) Cape Cod is great - I really like Provincetown (at the very end.) Ogunquit, Maine has beautiful beaches and cute atmosphere.
Quick Tips:
Best time to go is in summer - try to avoid graduation weekends (end of May, early June) - really hard to find hotels and they are really expensive then. Also try not to go in October - busiest month for hotels - they charge the most that month (I used to be a Reservation Manager at a hotel in Boston - I know.) If you are having problems finding a hotel, call the Convention and Vistors Bureau and they may be able to tell you who has rooms.
Best Way To Get Around:
Best way to get around it by the T (subway) - it is a little slow but gets you about anywhere you need to go. Parking is not easy - and right now - with the "Big Dig" (major construction throughout Boston), I wouldn't recommend a car. Taxis work well as well.