Sorry if I'm being repetitive; I didn't read the whole thread.
If you want to volunteer at a hospital, there are a ton. Within a couple blocks of Harvard med are Brigham&Women's, Beth Israel, Dana Farber, Joslin Diabetes, Children's, etc. There's also MGH, and its associated clinics (like eye&ear), which is accessible on the red line, or from a shuttle that stops at Brigham&Women's and the Prudential Center. All of the hospitals that I know take a couple months to get approved, and they expect 6+ months of committment, so that might not work out if you're only in Boston for the summer. It doesn't hurt to call and ask, though.
I'll be volunteering at a hospice in Cambridge this summer, but I also go to school here, so I was able to commit to a full year.
I think you might have better luck doing non-clinical volunteering, given your time constraints. I can give you the names of various volunteer organizations in Boston if you pm me. I'm the pres. of my school's community service organization, so I've got some ideas for what you could do in a non-clinical setting, or some places you could volunteer on a one-time basis if you want a little variety (like homeless shelters, elderly homes, neighborhood programs for kids, etc).