If can't make a red sox game - you could still do a tour of Fenway -- at least you get to see the park.
Some other things I like -- habor cruises --- you can take the cheaper route and instead of doing the touristy harbor cruises, you can take the ferries that go to the islands... fun just to visit a couple of the bigger islands (think picnics and exploring forts).
I love to just walk around the north end - get a coffee/desert and pop into a restaurant that appeals to you. If you see someone that looks like a local - ask them for what restaurant they like -- I've done that myself before even living in the area and have yet to be disappointed.
If you do love sports and are mobile meaning with car - you could always try a minor league team -- there is one in Brockton and one in Lowell - my guess about a half hour drive to either.
Also - look and see if there is anything on the esplande - often times there are concerts or movies.
Many things could depend when you coming -- there are feast days in the north end; all sorts of stuff that goes on.
If you want to venture out of Boston - nice areas to visit - Rockport, Plymouth, Salem. I love Rockport, personally - small seaside town.