Lived in Boston my whole life and there's not much that you should do that hasn't already been said..
For renting a car, I'd say go for it, even if it's for 2 days. Seeing New Hampshire and Maine would be great this time of year. Salem, MA is a great day trip spot to walk around and is a pretty historic. Also a mom & pop game store there called Game Zone you can check out, as well as a comic/collectible store called Harrison's. Salem Willows will give you a good look at the ocean as well as a few great food spots, a nice park and arcades. Foliage in New Hampshire (lakes region) can be nice.
For food, you're going to want to check on Pizzaria Regina, original location in the North End, but also another location in Medford, MA. If you like ramen, Yume Wo Katari is a no brainer. Honey Dew Donuts is by far better than Dunkins, don't let anybody fool you. For Mexican? Border Cafe in Saugus, MA or Burlington, MA. For super cheap, but good food - check out The Pour House on Boylston Street (Prudential, Newbury area). For breweries, there's a ton that popped up in Salem, MA also. Boston Beer Works is there, Notch, Far From the Tree, and Gentile are located there.
Downtown Boston including the Prudential building, Newbury Street, Boston Garden can all be explored and done in a day without much effort. I never went clubbing or anything, but seeing shows at Brighton City Music Hall were the best. Harvard Square, Central Square, Union Square - lots of stuff to do and check out as another day trip. Also close to MIT.
