My favorite are of Boston is Cambridge. Lots of cool places to hear good music. Lots of good restaurants. That being said it has been awhile since I was there but I cannot imagine too much has changed.
Lots of cool things to do in Austin depending on your tastes. Live music every night and a lot of variety of music as well, many excellent restaurants (again variety), the green belt to hike, many nice parks, lots of cool, funky stores, friendly people. I know that this is a general list with no specifics but there is just so much there. Here is my biggest hint, the best stuff and most fun stuff is in South Austin, so if you visit stay in south Austin and hang out there.
I have only been in Boston for about a week in 1997, but I loved the city. I had actually planned on moving there after school and spent the summer in Provincetown so that I could be close (I had a job there), but Boston was too expensive for me at the time. My favorite part of the city was Cambridge. Lots of neat things to do there and lots of cool people there. Also if you like to listen to live music there are a lot of good clubs there for that.