What is a "Good Place to Live" is very subjective and it is the kind of question that gets agents in trouble. You need to decide if it is a good place for you. Antioch has been having budget problems and cut backs in city services, but then many cities have. I myself am positive about Antioch's future and think homes in Antioch offer good potential. Also lumping every neighborhood in Antioch into one category (good or bad) is not fair. There are real differences between many neighborhoods in the 94509 area.
I suggest you check the school web site below. But even that can be deceptive. The real question is how will your kids function in the schools, not always how the kids are doing as a whole.
Get an agent that knows the city well and discuss your particular needs with the agent. That agent should give you a good idea of what areas will work for you.
I do a lot of business in Antioch and would be happy to work with you if you do not have an agent.
Below is a link to every home in Antioch 94509. You can search other areas if you follow the links.