I stayed at the Holiday Inn Dowtown-Port of Miami. It's like a $6 or 7 cab ride away from the hospital/campus (5-10 minutes during rush hour). Nice hotel....$80-$90 a night. The big plus, particularly if you get in early, is that the "Bayside Marina" is across the street. Place has a bunch of shops, restaurants, bars, live music to you can unwind a bit very close to your hotel.
Good luck