My first thought is to do Priceline and bid on a 3* in the downtown zone. Most of them can be had for around $55 to $70. You will probably get the Radisson, Hyatt Regency, Maririott or Dobletree Grand. I don't think any of them have free shuttles to the port but a cab is less than $10.
The Radisson, Doubletree and Marriott are all on Biscayne Bay and have rooms with port views. The Hyatt Regency is not on the bay but is a nice location and a very nice hotel.