First a few guidelines - Mexico City is at a high altitude, over 7000'. The air is dry, thin and polluted. If you aren't accustomed to high altitude, allow a day or two to adjust; I live at sea level so when I visit I always get headaches or experience the occasional bloody nose. Drink lots of water (bottled!) to stay hydrated. Sunscreen and lip balm are also suggested.
Mexico City, in Mexico, is often referred to as "el D.F." (in Spanish: el day ef-ay) which stands for "Distrito Federal". Or people just call it "Mexico", short for "la Ciudad de Mexico". Not to be confused with the next door State of Mexico or the country itself, which is often referred to as simply "la Republica". Why is this important? If you're planning on taking a bus out of town and want to get back to Mexico City, then you look for buses to Mexico, even though you're already in Mexico
.
Manners: Mexicans are somewhat more formal in nature than us "norteamericanos". Feel free to practice your Spanish, at least the greetings. Always greet shop and stall owners, thank them when leaving. When buying something, hand your money to the cashier. Tossing money on the counter, which we do at home without thinking twice about it, is considered rude. At restaurants you will typically need to ask for the check ("la cuenta por favor") - the table is yours until you decide to leave and to give you the check before you are ready for it is a no-no. (although I've noticed that at some places that cater to tourists the waitstaff will present the check without asking since most tourists aren't aware of this custom). And splitting checks is called "going American" by Mexicans and is not cool.
In cental Mexico City you might enjoy exploring the Historic Center ("Centro Historico") and Zocalo (main square). There is a hop on/off tourist bus that services the area along with other attractions which is a fun way to get a general city overview. On the Zocalo is the Catedral Metropolitana, a cathedral built by the Spanish conquistadors using the stones from nearby Aztec pyramids. Speaking of which, right next door to the cathedral are the remains of the Aztec's Great Temple, originally built in 1375 and discovered only in 1978. The Mexican national Congress building also flank the Zocalo. There are several restaurants with roof-top patios overlooking the Zocalo which can be quite nice for a leisurely lunch with a view.
The National Anthropology Museum in Chapultepec Park is world-class and worth seeing even if you have a cursory interest in the topic. The Zona Rosa (Pink Zone) is still popular as a destination for shopping and dining. Consider splurging at one of Mexico City's finer restaurants for at least one dinner; many of us Flyertalkers favor "El Cardenal" (you can find their website). You'll get great food and top-notch service at a reasonable price. For a quick, decent coffee-shop type of meal I like any one of the many VIPs restaurants that can be found nationwide.
I do eat at street taco stands and have only gotten sick once after over 25 years of traveling in Mexico. Rule of thumb: Look for lots of customers, which means food turnover and popularity - also make sure whatever you eat is thoroughly cooked. Mexican stomachs get just as upset as foreign stomachs! However I do not drink tap water or any of the juices sold on the street.
Ask at your hotel if there is a nearby "tianguis" (tee-an-geez) or neighborhood flea market they recommend that you can visit. These spring up overnight for a day; residents like to shop at these for everything from clothes to fruit to toys, etc. Haggling is expected.
For more upscale shopping (no haggling
) there are modern shopping malls throughout the metropolitan area. Mexican department stores such as Liverpool or Paris Londres will seem familiar other than the language, but you may notice that sales staff are much more service oriented than what you are used to back home. For example buy a pair of nice dress shoes (Mexico makes some great leather shoes - many shoes are manufactured in the city of Leon) and you'll see what I mean.
A day trip visit to the town of San Juan Teotihuacan to climb the pyramids is something that shouldn't be missed. You really don't need a guided tour, you can easily do this yourself. And if you go on Sunday, I believe admission to the site is free. Getting there is easy, it's about 50km northeast of Mexico City. Either catch a bus from the Central de Camiones Norte (North Bus Terminal) in Mexico City - look for the bus line that services Mexico-San Juan Teotihuacan. Make sure they sell you a ticket to "Los Piramides". Alternatively get yourself to the Indios Verdes metro station and catch a bus to "Los Piramides" from there. One way fare is about three or four dollars if I recall correctly.