As long as you have a car, you don't have to live right near SM. I lived in South Pasadena for years and worked in Malibu... it was an awful commute, but I did it... The further east you go, the cheaper rents are. I also lived in a predominantly hassidic jewish area in West LA (Robertson and Pico, there's also a Kaballah center there) and I LOVED IT!!! The rent wasn't exorbitant, and you are within walking distance to lots of restaurants, etc. You still NEED a car, though... LA is so spread out, it's hard to find a place near a grocery store LOL!!
You could also try the Wilshire district (near LA County Museum), there actually *is* a grocery store over there, and Pasadena if you don't mind a horrible commute.
LA is a great place to live, but it will take some getting used to coming from AZ. If you live in Pasadena and commute to SM depending on what times you are commuting, it could take anywhere from 30+ minutes (off peak times, no accidents, etc.) to 2+ hours (Thanksgiving eve... rain... ugly). From Robertson/Pico area it will take about 15 - 30 minutes depending on how you go (surface or freeway) and how much traffic there is. Traffic will ALWAYS be a wild card because you just can't know what is going on at any given time.
I totally understand the moving thing... between dh and I we've moved 20+ times in the last ten years... I HATE MOVING!!! (but am considering doing it again soon if we can find a house we like better than this one! Call me crazy!)
PM me if you want any more info. I lived in LA for almost 20 years (up til about four years ago)... I'm happy to help!