The congested streets of Zona 1 have a reputation, not completely undeserved, for being unsafe—many visitors avoid downtown Guatemala City entirely—but with a few precautions and a lot of common sense, you can visit or stay in the historic center with minimal worry. A few hours should suffice to see the Old City sights, depending on the time spent in the Mercado Central labyrinth. Here are some tips:
Ask hotel personnel for the lay of the land. If you're staying in the city center, get that valuable where-to-go and where-not-to-go advice from those who work at your hotel. They know the neighborhood better than anybody.
Carry as little as possible. The standard no-flashy-jewelry, minimalcash, well-hidden money-belt advice applies. Carry a photocopy of the pertinent pages of your passport, and leave the original in your hotel safe if possible.
Walk purposefully. Look like you know where you're going, even if you're hopelessly lost. Standing on a street corner with a puzzled look and your open Fodor's guide brands you as a tourist. Pop into a store or other public interior to get your bearings and ask for directions if you need to. Your best bet is to duck into the cathedral, sit in a pew and map out your route (and perhaps get a bit of divine guidance).
Take taxis, especially at night. Whether you're staying or just visiting here, at night, travel by cab, even for very short distances. Your hotel or restaurant will be happy to call one for you.