Hey, 2nd year med student here. I drove up from NY for my interview as well. Yes, you can leave your car in the garage on Albany St and Concord St. I think it's $30 or $35 max for 24+hrs. I also stayed around to experience a bit of Bahston. I jumped on the silver line (SL5) at Washington and Newton and took it down to Downtown crossing, walked through downtown, through Quincy market, and went to the Union Oyster House. I sat at the U-bar, had some shucked oysters and their awesome clam chowder (oysters were kinda expensive tho). Then I took the orange line from Haymarket or State, transferred to the silver line at Tufts (SL4 or 5) and got off at the same stop at Washington and Newton.
If you want to do some walking, I suggest walking to Copley Square (such pretty streets around here with rows of brownstone buildings). You can see Trinity Church, the Boston Public Library, etc.
To be the ultimate tourist, you can walk to the Prudential Center and go on a Duck Tour. I think it's $27+tax for a full time student and lasts 80mins. It goes everywhere in Boston and into the river. I would buy the ticket in advance so your specific time doesn't get sold out. Even by yourself, it's a lot of fun and a great way to get pictures of Boston, especially from the Charles River. Quite breathtaking if it's good weather.
Finally, you can also go on some self-guided walking tours of the South End. Check this out:
http://www.walkboston.org/
Hope this helps! Have fun!