The Conrad. This may be more expensive than what you want, but we liked it a lot, I can't recall how much it was due to it being incorporated into a cruise line transfer package but we thought it was reasonable at the time. What I really liked upon arrival was that when we got to the hotel early in the morning, 8:00 AM, they checked us right in with no fuss or grief which eliminated the inconvenience of us having sit around half the day while the room was being prepared (after having traveled for 20 straight hours). Gave us a chance to take a short nap and then explore the city. We checked out at noon the next day and shortly after were off to board our ship.
It is located in the center of a nice high-end clean location down-town in the financial district but very close to the cruise port on Biscayne Bay. Lot of quality places to dine close to the hotel as well as the fine restaurant in the Conrad.
In particular we were impressed by our room and the terrace overlooking the Bay which is located off the restaurant and lobby. The lobby is on the 20th floor if I recall correctly. It is sort of awkward getting to one's room as you must ride the elevator from the ground floor up to the 20th then change over to another elevator regardless if you are below or above the 20th floor. I'm certain they do this for security purposes.
They provide free complimentary internet and continental breakfast off the restaurant. In the evening one can sit out on the patio and enjoy a cocktail while looking over the serene waterfront area and nearby bay. We could see our ship from there.