Well, the best shot in Longwood would be BIDMC. Brigham may give you a shot if you play like you want to be a nurse. Dana Farber may be an option but I have no background there so I can't give any advice. NE Tufts medical center has a more person interview process for their ED tech position if you have experience and Mass General is always a hot spot for would be volunteers. If you are looking for a more inner-city feel then try Boston Medical Center.
If you are willing to travel to peripheral areas the Whidden Hospital in Everett would be an excellent choice. However, there is also Cambridge, Mt. Auburn, Melrose-Wakefield and Lawrence Memorial. That almost covers the north side without mentioning the west or south. If you are willing to try and get experience there is a **** load of hospitals in and around Boston. Hey, you could go to the north shore and work at Lahey if you want.