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Any trip to Mexico City has to start in the Zocalo, the ancient hub of the colonial city. Filled with throngs of people, it still maintains a deep resonance with the centuries. Visit the awesome national cathedral and the Palacio Nacional to see Mexico past and present. The Aztec past can be seen at the Templo Mayor, just around the corner. This ancient temple was only recently rediscovered after 500 years. Well worth gaping in amazement.
For dinner, be sure to call ahead or you might not get a seat at Izote, one of Mexico City's more outstanding restaurants. Located in Polanco (the Beverly Hills of Mexico City), the restaurant perfectly updates the classic Mexican recipes to mouth-watering luxuries. The ceviche is particularly awe-inspiring.
4. National Museum of Anthropology (Museo Nacional de Antropologia)
Spend the next morning shuffling through this incredible museum, filled with the relics of all of Mexico's ancient cultures, from the Aztecs to the Zapotecs. It can get very crowded late in the day, so the earlier you can go, the better. It's honestly one of the world's truly great museums.
Take a break from ancient artwork by shopping for new stuff. The Saturday market in San Angel in the southern outskirts of town is filled with arts, crafts, furniture, music, and taco vendors. While the prices aren't as rock-bottom low as other markets in the city, the quality is excellent, and coming from New York or LA, everything will seem like a bargain. Find something cute for your home, but be careful. I met an armoire here that nearly caused me to redo my entire bedroom.
6. Aguila y Sol
All that shopping will work up an appetite. Fuel yourself with dinner at another of Mexico City's truly gourmet establishments. This is updated Mexican soul food. I had a filet mignon that was as tender as any I have had in any country, and it was perfectly matched with a chipotle sauce that sent my taste buds into orbit (in a good way). The hibiscus flower margaritas will make anyone weep with joy. Again, be sure to call in advance.
Before you catch your flight back to the States, you do need your exercise, if for no other reason than to burn some of those delicious calories. Take a half-day bus tour to Teotihuacan, a mysterious ruined city of pyramids north of town. The city has been abandoned centuries before the Aztecs arrived. They called it the "city where men became gods" and you'll feel the same way when you climb to the top of the Pyramid of the Sun and stare out across the valley. It's a magical place.