

Either choice will be expensive and you won't get to see anything around the city but at that time in the evening there's not much you can see anyway. So I think you'd better just stay at one of the hotels adjacent to the airport and have dinner there, or alternatively at one of the "bigger/nicer" restaurants within the airport. if you stayed somewhere outside the airport area it could take you quite a while to get there and the risk of missing the flight is real. Then you have to go back to your hotel and 9 AM is exactly when mostly everyone's work day starts so the rush hour starts by 6 AM. Most places to have dinner close at 10-11 PM so if you have to check-in & drop your luggage at the hotel (preferably next to the airport as Extra-distance suggested) and then take a taxi to go to the "popular" areas where you could have dinner (Polanco, downtown, Reforma, Zona Rosa, Condesa) you'll get there by 9-9:30 so that doesn't leave you much time to relax at the restaurant. That's too little time (and already "late" at night) to really go anywhere outside the airport area, which isn't too far from downtown if you draw a straight line but with the city traffic it can take you a while to go and get back from wherever you decide to go.
