Bring clothes to layer. It's actually not that bad here the last few days. Tomorrow will be in the 40s, which is extremely mild for this time of year. It probably won't last though.
Definitely check out Harvard Square. Lots of shops and interesting people.
Government Center is a good place to check out as well. Fanieul Hall has lots of shops, and there's some good places to eat around there.
We have some good museums there. The Isabella Stuart Gardiner (I think that's the right name...It doesn't sound completely right to me right now for some reason), and the Museum of Fine Arts are worth a visit.
If it's nice out, Newbury Street is always a good walk. Lots of little shops and boutiques. Great window shopping and lots of personality.
And of course, the Freedom trail hits most of the great historical monuments/buildings in the city. If you're not good with cool weather, you may not want to follow it around town. Any decent guidebook can tell you what each attraction is, so you can pick and choose if you like.