Most of the tourists don't use pesos, just dollars. But certain type of tourists enjoy buying in the farmers' marker, or taking buses instead of taxis, and they'll need pesos. You can use pesos also to buy books. Buying a package tour will of course reduce the amount needed daily. Carrying traveler's checks is better than carrying cash, but have enough cash for meals and taxis.
Many people find that carrying lots of one-dollar bills is helpful, primarily for use as tips.
Only non-U.S. credit cards are accepted. Banks and hotels accept Travelers Checks from all countries, but not American Express. There are rumors that banks and hotels now accept American Express travelers cheques because they can be cleared through Canadian banks, but to be safe, don't use them. It doesn't matter what your citizenship is. Some people have bank accounts in England, Mexico, Canada, Israel, etc.