The Los Angeles area is actually of numerous cities. There is the city of Los Angeles, then there is a city like Beverly Hills that has it's own police, fire, etc.
Police departments are required to track crime statistics. Most have them available on their websites
I looked at the Beverly Hills Police site, no crime stats at all.
I did find a nifty site (see link below) that does provide some information.
So far as "average price of a two bedroom home", that varies a great deal. Trulia is a very good resource to provide recent average sale prices and sale price per square foot.
From the REALTOR perspective, the biggest determinants of home values are:
proximity to desired destinations
Quality of the city public works (roads, utilities, and other infastructure).