For a current actual for events that don’t suck, check The Boston Calendar. A totally different kind of events, happening at Harvard Law School, is available here. Obviously, Berkman center’s calendar of events is something to follow as well (ok, this is not exactly the entertainment part).
Whale Watching is something definitely worth considering.
Also, remember to take advantage of your student ID and go to Harvard museums – they have amazing collections, often surpassing many national museums around the world (while it is somewhat shameless to observe that they don’t know what to do with the money, it still is great to visit great, and often uncrowded museums): Harvard Museum of Natural History (here) (to see a skeleton of giant sloth), Harvard Art Museums (also near the yard) (to see lots of expensive paintings barely watched by anyone), Peabody Archeological Museum (to see Northern American relics and other excavations), or Semitic Museum (Eastern archaeology). Whenever you shop in a museum store, be sure to flash your Harvard ID for a discount.
If you plan to go to regular museums, check out the membership programs – some offer privileges in museums in other cities and may turn out to be more affordable than just entry.
Revere Beach is accessible by subway, but that’s where its advantages end (it is a bit in the boondocks, not particularly clean, with no attractions or services – definitely not recommended). For a longer trip it may be worthwhile to take a ferry to Cape Cod (don’t go by car, the traffic will kill you!), or drive to Ipswich to Crane Beach (Kaede is a nice, simple B&B with Japanese flavor to consider). Also, taking a ferry to Provincetown may be fun!
If you’re a sailor, or if you’d like to learn how to sail, there is a great opportunity for you at Community Boating in Boston. For little over 200$ PER YEAR you can take lessons and rent yachts (as well as kayaks, windsurfing boards, etc.) as often as you want! This is really amazing, and probably the only occasion when a community club offers something even more attractive than the vast resources already provided by Harvard. Getting to the club is easy, since it is just by Charles/MGH red line T station.