Nothing eases a traveler's need to get around efficiently while enjoying the trip like a basic knowledge of the language of the land. Locals in Mexico tend to be friendlier and generally more helpful when you smile, show patience and try to communicate in their language. Spend a couple of weeks with an audio course in Spanish or buy a phrase book and practice. You'll get more enjoyment out of your visit.
Mexican banks are perpetually understaffed to meet customer demand. As a result, you can expect incredibly long lines waiting to see a teller about changing some dollars into pesos for you to spend. You might get the best exchange rate in town by changing money at a bank, but is it really worth a few extra centavos to wait an hour in line? Your hotel will probably have a counter where you can exchange money at rates favorable to the bank down the street. If you have to pay a little more, consider the savings in time you'll have to spend sightseeing. It's worth it.
You won't need a passport to enter Mexico, but you will need one to get home if you live in the United States. New laws effective June 1, 2009, require all individuals entering the United States by air to hold a valid passport. To enter Mexico, you will need a travel permit, which your airline will furnish as you approach your destination in Mexico. If entering by car, you will complete the form for a travel permit at the border crossing. Keep your documents safe. it is also a good idea to carry them with you at all times. The best way to do this is with a passport pouch or zippered wallet that you wear around your neck or secure under your clothing and around your waist with a Velcro strap.
The crime rate in Mexican cities is no better or worse than in any major metropolitan city in the United States or Europe. Use the same common sense in Mexico City as you would follow in New York City, and you should have no problems. It's not a good idea to walk alone at night. As a precaution, you might want to have your restaurant call a reputable cab company when you are ready to return to your hotel for the evening, rather than jump in the first available taxi on the street.
Be sure to travel with any medications you use daily, and pack enough to last the duration of your trip.
Avoid drinking local tap water. Buy bottled water and be careful of eating any raw fruits or vegetables that may have been washed. As a rule governing consumption of fruits and vegetables, if you cannot peel it, don't eat it.