I'm currently a freshman at Northeastern University one of the classes I'm taking is Boston History. We've done 4 walking tours this year through Boston and this is what I would recommend.
Definitely Head over to
Fanuiel Hall and the Quincy Markets. The best T stop to use to get there would be Government Center.
After that walk over to the north end and walk down Hanover st. Mike's Pastries is an amazing pastries shop, excellent cannolis. There are numerous other pastries and eateries also located on Hanover st. Also the
Improve Asylum is an extremely funny show.
If shopping is more your interest then Newbury St. is where you want to go. Many shops to choose from.
The Boston Common and the Public Garden are both nice places to walk through and relax.
Hope that this information helps.