NOOOOOO...I know you're a mileage addict but you can't come down here and stay at the airport. Trust me on this. The airport is boring and the neighborhood surrounding it totally uninteresting and not particularly safe. If you want a little local flavor and don't want to pay very much, stay downtown by the Zocalo (try the Hotel Majestic or Canada). For something also very affordable in a great residential/business/restaurant/shopping area that's within walking distance to Museum of Anthropology and Chapultepec Park, try the Hotel Polanco in Polanco. Either way, you'll experience being in the middle of a fascinating city instead of a soon-to-be-mall, which is what they're turning the current airport into after the new one is built. Polanco also has chains like Intercontinental, Nikko and Marriott if local hotels don't do it for you.