I go to Fenway Health, too. They're wonderful there. My doctor is extremely friendly and fun to talk to -- I love her! The phlebotemist I usually get is also a wonderful person; she makes me laugh every time and she always makes sure to use a butterfly needle, so I barely feel a thing.
Oh, and there's a Burger King right next door. I usually get a chicken sandwich while I wait for my appointment (I always get there early). It's just a really convenient location. The subway gets off at Fenway station, which is barely a 3 minute walk from the hospital and you only have to cross two streets.
As for friendship, I'd offer but I'm all the way in Stoughton (it's next to Brockton). I'm really pretty far from you, but if you ever want to coordinate appointments or something, I'd be open to that. I don't have any friends like us, either, so I know how it can be to be lacking; I really hope you find some soon.
Anyhow, I think you're in wonderful hands with Fenway. I wish you the best of luck!