There are few options but they all involve arriving in the mid- or late-afternoon and departing at 10AM next morning (be at the airport by 7:30AM?). So it is mostly the night time there. Other than grabbing a dinner, I don't think there is any tourism angle to explore. That is why I am looking at it as a transit through AMM airport and not a stopover in Amman city. So a clean and safe place to sleep + shower would be my goal. A hotel right at the airport would be good, although cost is always a consideration and I would be ok with a short taxi ride.