depends what you want to do
1. Seaport is one place i recommend especially now they are building lots of new attraction there. King's bowling is new and is kind of nice (it's more of a bar than anything), and if you walk a bit further down by Del Fresco's, beautiful view, also lots of bars and restaurants
2. Go to Cambridge, visit Harvard, literally lots to do.
3. Prudential/Backbay area, you can pay to go on Duck Boat tours to go around Boston, and you'll also get to go on the Charles as well
4. I'm usually a sucker for museums wherever I go so if you've never been, and also like that kind of stuff, Museum of Fine Arts is another destination i recommend.
5. Not to sound bias since I'm Asian but have you thought about food in Chinatown
6. Fenway! even if you're not watching the Sox, that area is still nice to walk around, plenty of bars!
7. Quincy Market / faneuil hall also close to the North End and some other historical sites!