Depending on the location of your job and your salary, living close to work may be incredibly expensive. OTOH, if your job is in a rough part of town, you probably won't want to live close.
LA is highly variable. To be clear, saying "LA" can mean a lot of different places from truly downtown LA to Sanbernardino to Santa Monica to Irvine. All of these places are different, with many different areas in between. You can be riding next to 2 million dollar homes one minute, then 3 miles down the road you are in the midst of poverty (where the houses only cost $450K

). There are many areas in LA that I would not want to ride a bike through.