Hmmmm.
I would try to stay at the Hyatt right in the terminal to get some sleep and rest a bit. The hotel is very nice, and has many amentities you would enjoy. You will essentially get of the plane, take a quick tram ride, and take the escalator up to the hotel.
I'll give some more thought to where else you might like to stay
FWIW -there is a possiblity I'll be there around the same dates. I'll keep you posted.