Crime stats in Antioch indicate mainly petty property crimes such as car break ins, cell phone theft, shoplifting and similar crimes. There is some street violence but that is typically a thug on thug type of thing and it is very unlikely that an everyday citizen is going to be assaulted or bothered walking down the street during the day or at night. In my opinion Antioch's biggest challenge and source of most of the petty crime comes from the youth under the age of 25. A small percentage of the kids in town cause most of the trouble.These troubled kids are "latchkey" kids with very little parental supervision. There is some gang activity but as I said, it is highly unlikely any of these elements are going to bother you.
Katie from Trulia here. You can find good info on recent crimes in Antioch with Trulia's crime maps: http://www.trulia.com/real_estate/Antioch-California/crime/