There is a lot to do in the city, one of the most interesting places is the antropology museum on Reforma in the Parque de Chapultepec, you need at least two days to see it all, and you can actually visit the remains of the original city, Tenoxtitlan, the ruins are located on the side of the cathedral on the main squake El Zocalo, the National Palace has interesting murals, if you have the oportunity to see the balet folclorico in the palace of Bellas Artes, before the show the front curtain is actually a stained glass window and they depict a sunset and night fall with lights in the valley with the volcanos as a back drop, then this enormous window lifts and the show starts, it is worth seeing it.
There is also the castle of Chapultepec and many more places, also some very good restaurants, you can also take a tour and lunch aboard a "Chinampa" on the canals of Xochimilco, just remember that the city is at high altitude 7360 feet above sea level, in the outskirts you will also find the piramids in Teotihuacan, for all of this bring good walking shoes and remember that it will be chilly in the morning and hot during the day and then it chills back down in the afternoon, Mexico is a desert what saves the city is the altitude, also remember to use a hat and do use sun screen, you can get a nasty sun burn in a few minutes a lot faster than at sea level.
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