Puerto Vallarta safety is quite good since it is a major tourist hub. The U.S. Department of State says that crime in Mexico varies widely by location with the worst crime reported in the states that border the United States and the south of Mexico, mostly because of drug cartel activity.
Homicides and other serious crimes are infrequent in major international resort cities like Puerto Vallarta, although the U.S. government has issued travel warnings for other areas within the state of Jalisco, primarily on its borders with the states of Michoacan and Zacatecas.
Crime such as burglary, pickpocketing and vandalism can occur at any time but is worse during major public and religious holidays in Mexico, like Semana Santa, the celebration of Holy Week at Easter when Puerto Vallarta is filled with tourists from Mexico and other countries.
You can stay updated on travel warnings and safety information at this U.S. Department of State website.