I would suggest looking at sites like WIOL or Travelnow and see what type of rates you can find for that night noting the location. We have done extra nights at the beginning and end many times and it can be fun to try new places. Maho plenty to walk to as well as down towards the Atrium area. Marys Boon sometimes has some late check out options but not much for food around there at that time of night.
Most of the options will be better than the Miami Airport Hotel, and it is nice to be on island.
Long time between now and then, likely to be some flight changes along the way.
Enjoy where ever you end up!
T
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