Have decided to book the MIA Hotel. Couple of sherbets on the plane, check in to hotel, dinner in the airport somewhere and with time difference be up and away by 4.30am the following day (assuming Avis is 24hr?).
Avis is 24hr at the airport, off-airport is daytime only.
Assuming you do really mean to eat
in the airport, the best IMO place is in fact in the hotel:
http://www.miahotel.com/amenities.htm . Everything else landside is finger food

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Bring earplugs for the MIA hotel; not so much the planes more the minimalist dividing walls.