Boston's tiny and you can easily see most of it in a few days. That's not saying you can't spend longer here, but you won't feel like you missed out on too much. It's also a fantastic walking city. The furthest walk you'd want to do, from the North End all the way down to the Museum of Fine Arts is only a little over three miles. That being said, the subway (or T) is easy to use and goes to all the areas you'd want to stop by.
Beacon Hill and the South End are my favorite parts of the city. Beacon Hill is within close walking distance of both the Public Gardens, the Commons, and the North End (the Italian district). There's loads of fantastic Italian restaurants in the North End, my favorites being Antico Forno, Limoncello, and Lucca, if you're looking for something a bit fancier.
If you're not from the New England area, or somewhere else with beautiful fall foliage, you might appreciate taking part of a day to go to the Arnold Arboretum. It's a great place to relax and enjoy some wide open spaces, but would require you to take the T a little outside of Boston. It's probably about a 20-30 minute T ride away from the center of the city.
The Freedom Trail is a great way to see some of the older areas of Boston. It's a red line literally painted/paved-in-brick on the ground and it leads you from the top of the Commons to the Quincy Market/Faneuil Hall up into the North End and over the river into Charlestown to see the Bunker Hill Monument and the USS Constitution. Do not that the Constitution and the Boston tea party boats, which are south of Faneuil Hall, are both under a bit of repair, so they are mainly covered in tarps.
EDIT: I see you're staying up in Watertown, a bit outside of the city. I'm not certain the best way to get into Boston daily from there, but I'm sure your hotel will have suggestions. If you do end up driving into the city every morning, spending the day in the city, and then heading back to your hotel via car after dinner or something, I have found the best rates at the parking garage underneath the Boston Common. See
http://maps.google.com/maps?f=d&source=s_d&saddr=100+N+Beacon+St,+Watertown,+MA+02472+(Super+8+Watertown%2F+Cambridge%2F+Boston)&daddr=Zero+Charles+St.,+Boston,+MA+02116+(Boston+Common+Garage)&geocode=CTB88i3m1uc3FVBthgId9eXB-yGX_iOfk8UptA%3BFRRHhgIdMZXD-yFg14xMZ3fn0w&gl=us&hl=en&mra=pe&mrcr=0&sll=42.337915,-71.346699&sspn=0.761333,1.399384&ie=UTF8&z=13.
I apologize I don't know how to make the url smaller haha.
Enjoy!