St. Louis is a great balance between the coasts. It is affordable and diverse, and your life can be tailored any way you like it based on where you choose to live. The metropolitan area is about 2.5 - 3 million people so it qualifies as a "big" city. The weather will be a bit of a shock to a California native but the upshot is that you get FOUR seasons and the Spring and Fall are phenomenal in STL.
Brentwood, University City, Richmond Heights, Maplewood, St. Louis Hills, Dogtown and The Grove tend to be the most popular, liberal, and diverse. Clayton and CWE are also really nice areas.