A few decades before my birth, but I'll give it a try....
I have gathered from watching I Love Lucy that there was a place called "The Brown Derby" that was portrayed as being a celeb hang out - I believe this was a real place. In that episode she dumps food on William Holden if my memory serves me well.
I also remember from a Bugs Bunny/WB cartoon about the Cocoanut Grove at the Ambassador Hotel - where they held the Oscars some time ago, as well as the Roosevelt Hotel (they now have a place called the Tropicana Bar, but I don't know if that existed back in the 50s). I guess sometimes watching the tube you actually remember some stuff
Other nightspots would include El Capitan and the Mayan, the Egyptian, and the Chinese Theaters at the very least.
Schwab's Drugstore has also been mentioned a lot, namely as a place where Lana Turner was "discovered" but I believe that is actually a false story. That reminds me, I need to go watch LA Confidential again...