The crime rate in San Antonio has gone down in recent years, and there's a strong police presence downtown (in fact, both the transit authority and the police department have bicycle patrols); as a result, muggings, pickpocketings, and purse-snatchings in the area are rare. Still, use common sense as you would anywhere else: Walk only in well-lit, well-populated streets. Also, it's generally not a good idea to stroll south of Durango Avenue after dark.
Crime -- San Antonio is a safe city. Violent crime occurs less frequently than in the average American city. In fact, of the 32 largest cities in the U.S., San Antonio ranked the eighth safest according to a firm that sorts through crime data for the United States. Still, you will want to avoid tempting fate by keeping off the low-traffic areas of the River Walk at night, and staying close to groups of other people. You also need to protect yourself from the opportunistic thief, especially purse-snatchers in the downtown area. Take care not to leave your possessions unattended on a chair at a restaurant or bar, and when walking around the downtown area at night, keep them tucked under your arm.
The other most common areas for visitors, the Monte Vista and King William neighborhoods, are usually safe to stroll around in late at night, but the same cannot be said for the area south of King William, which closes down early and doesn't have many pedestrians at night.