Here's an idea for your Tuesday arrival:

Drive half way to MIA via Port St. Lucie, Florida (about 120 miles / 2 hours). There is a Courtyard on the beach there (Courtyard Hutchinson Island Oceanside ). I haven't stayed there, but the location is about perfect for your needs. Spend the day relaxing and then another 120 miles to MIA that evening.

If you want to drive further, there is the Marriott at Delray Beach and a several Courtyard/Marriott/Renaissance waterfront properties in Ft. Lauderdale. Any of the inland properties would be dull, in my opinion, unless all you wanted to do is sleep.