Hi there Scott. Thanks for your question! Almost every part of Los Angeles is under rent control, so you will most likely be under that, however some cities are more strict than others. West Hollywood for example is, i believe 3%, where as Los Angeles is 5%. Do the research and get the exact numbers from the cities themselves.
In general though, the best place to own a rental property is the ones that have the strongest rental market. I would recommend USC area, however I doubt you want to live there so not for an owner occupied situation. Hollywood, Los Feliz, and Silverlake are very active rental markets and bring the strong rents that will pay your mortgage for you. I would stay away from the valley as the rents have dropped a good bit.
If you buy a really nice building that is marketable, you can get solid rents and will have longer term tenants that will enjoy living there. So I always think that makes a big difference.
I would love to meet with you and find out your goals so I can give you more specific advice. I'm an expert on the rental/income property market, and I have lived in Hollywood, West Hollywood, Silverlake, and have my office in Los Feliz. Please contact me anytime through my website below. Cheers!