I would add:
Check out the North End for old-school Italian. I was told that there are people who've lived there for 50 year who still can't speak English. Mike's Pastries is said to have the best cannoli, though others dispute this and I have no opinion. Hanover Street has many good restaurants.
Also, head over to Charlestown and see the Naval Yard, Old Ironsides and the Tavern on the Water, which has one of the best views of the downtown skyline of any restaurant (you can also get an interesting view from the Federal Courthouse, which is also very interesting architecturally).
Another little neighborhood close to downtown: Beacon Hill. You can walk around and check out the old brownstone row houses, and if you go down Charles Street between the Boston Common and Cambridge Street there are many "cute" (my wife's term) little stores and restaurants. A very good restaurant in that area that I highly reccommend (I know the chef, but I'd reccommend it anyway) is 75 Chestnut (the address and the name of the restaurant).
Another good hotel downtown: The Langham. It's in the old Federal Bank building, and even if you don't stay there you should head to the piano bar for an overpriced drink to enjoy the ambiance and the architecture.