Nice question. Generally, the metro area is quite safe. While there isn't a "bad area of town" to avoid, some areas have lower or higher crime rates than others. Generally, the highest crime rates are in Glendale, South Phoenix, and West Mesa, but even these areas have crime rates that are far lower than bad areas of most other major cities.
Petty crime is generally not a problem, although you should take standard precautions like locking your car and not flashing expensive jewelry around. Even so, thinks do sometimes happen. Fortunately, there is a capable police force to assist.
As a tourist, you'll spend most of your time in Scottsdale, downtown Phoenix, and Tempe. These areas are fine.
