Holiday Inn near the port (downtown area) you would still need to get to this hotel with a taxi, so you dont gain much even though it does have a port shuttle. It was running about $159 when I was there last time. It is a favorite of cruisers and there will be a lot of other cruisers staying there more than likely.
Im thinking your best bet would be a airport hotel that also has airport pick up?
Here are a couple of ideas
Homewood Suites in the Blue Lagoon area near the MIA airport meets most of
your needs. Big rooms, great breakfast, nice pool area, and free airport shuttles. Plus they offer a free manager's reception Mon - Thurs and there are shopping and dining options in the nearby strip mall.
La Quinta Miami Airport North. There is a free shuttle from Miami Airport, and a group shuttle to Port of Miami for $10. The neighborhood is relatively safe but not much to look at; it's got ethnic restaurants, gas stations for cigarette and beer runs, and fast food places.
Hilton Miami Airport Hotel. Free shuttle from MIA airport.