I'm checking out the same thing but I want to leave my car there for the week. Anyway the Holiday Inn Express in Miami CTRL Miami Spring 88 dollars a night they also have a shuttle for a small charge to the Port of Miami...sorry they don't tell you the charge on the web site. So far they are the only ones I can find that goto the Port vice the Airport.
I have been researching this also. I cruise in September. I found a website called www.parksleepfly.com It gives options for parking. There are not many offered. At this point I am leaning toward using the Rodeway Inn and their package for $114 which includes shuttle service both ways.
“Twenty years from now you will be more disappointed by the things that you didn’t do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover.“
Red Roof on Le Jeune, left car there 1 week, transport only to the port. After the cruise, $27 for a cab back (not per person). It's across the street from the airport so flight patterns were noisy every few minutes while outside, muted while inside.