One hotel around not too far away from the Port is The Hotel Sofitel. It is actually around the airport. So, it is about 8 miles from the Port of Miami. They provide free courtesy transportation to and from the airport. As for transportation to the port... you would have to call them. I used to work at Miami Intl. Airport and would always hear good things about the Hotel Sofitel.
If this is your first cruise, make sure to visit this website often and read up on all the advice. Here is some links to articles on this website for 1st time cruisers (click on the word) :
Booking Your 1st Cruise
Cruise Packing List
And speaking of what to bring on your cruise, make sure to bring a positive attitude. Then you will almost be certain to have a good time.