I volunteer through the Medical Career Exploration Program at BWH. It gives you patient contact from day 1. I know that most of the hospitals in Boston (at least BI, MGH, and BWH) have similar programs--but sign up NOW for orientation because they fill up months in advance.
Tufts School of Medicine also runs a free clinic in Malden (T-accessible) once per week. It's even better clinical exposure, I think, but since there is only one night per week to choose from, it's a little more difficult to make it fit in an undergrad student schedule.