Good Under 21, Great 21+ – A lot of people complain that there isn't much to do until you're 21, but it all comes down to what you are really looking to do. If it's party, there's always parties given the massive number of students in the area. If it's cultural, go to the theater district, or head to Chinatown for dumplings, or visit the North End and stop at Mike's for a cannoli. And if it's a nice Fall or Spring Day, go outside and sit on the quad, walk the city, visit Boylston and Newbury Street. There's definitely no lack of things to do.
Of course, if you find yourself in the legal majority (21+), feel free to scout out the many bars and clubs throughout the city. If you're under 21, stay clear of the bars and clubs, especially if you're a guy. Bouncers are just as likely to keep a fake ID as they are to call the cops and ruin your semester for you.
Of course, there's always the sports. You'd be hard pressed to find a more vibrant fan base than in Boston. Watch the Celtics at the Garden. Take a trip to Foxboro to see the Pats play. And of course, you can't miss going to a game at Fenway (and this is from a Yanks fan). What it boils down to? If you can't find something fun to do in Boston, pretty much every day, it's probably no one's fault but your own. :)