Not knowing what you want to do or where you want to live, I second the recommendation of checking out Craig's list. Also, if you drive around you will find a lot of independent management companies you can call to get information from. I don't know where you want to live, but if you want to be on the westside, my management company is fairly reasonable. Most of their buildings are older, postwar types. Here is a link to their
vacancy list.
Feel free to PM me too. I've lived in LA most of my life.
LD