I think if I had only that amount of time and I felt really compelled to get a taste of Mexico City I would take a taxi (tourist or sitio taxi) to Zocalo Square as mentioned (200 pesos). From there you can walk straight down one street about one mile to the Sheraton Centro Historico hotel where you can get a tourist taxi back to the airport (260 pesos).

The walk is safe, usually crowded and filled with lots to see.