Trinity Church on Copley Square. Sunday mass was going on, and I'm not religious so I didn't have a chance to step inside. But the outside is impressive. My good deed of the day was helping a mom with two kids cross the street to attend mass. 
Faneuil Hall and Quincy Market. Great place for sunday brunches. 
Harbourfront with live music. You can take a ferry from here to Salem, Cape Cod or other tourist spots nearby.
Good ol' Hah-Vahd. My good friend and former Ph.D. colleague is currently doing his post-doctoral studies here. I am so proud of him! I couldn't go through with it. After 7 years of graduate school, I was done. So I got a job instead. I don't regret my decision though. It sure beats being a poor student/post-doc!
