Locals will have better ideas, but things I would recommend:
* Duck Tours. It will probably be pretty cold, but these are a great way to see the city, and usually the conductors are very entertaining;
* The Aquarium. Pretty self explanatory, but if you're into aquariums, this is a pretty good one. Check out the Imax if anything cool is playing.
* Shear Madness. If you're into comedies, this murder mystery play is a really good time.
* Eat in the North End, and then check out Mike's Pastry. Some will tell you this is overrated, but I disagree.
* If you're in the mood for a high class dinner, go to Grill 23. It's an amazing steakhouse.
There are dozens of great bars and pubs to hang out in; if you're into live Irish music, the Black Rose in Faneuil Hall is usually a pretty good option.