I didn't spend too long in the city during my spell in Mexico, but you're near enough the Zona Rosa there, which is a good area to go out providing you're not bothered by being hassled by people touting for strip clubs (at the tamer end - prostitution is legal in Mexico City) every twenty feet or so. The Centro Historico is worth exploring, particularly the Zocalo - the huge main square - which is flanked by the biggest cathedral in Latin America (maybe even the biggest in the Americas, I forget), and a couple of minor pyramids behind it. There's usually something going on in the square itself too.
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