In Los Angeles we had KRLA as Sectmaniac pointed out. It was an oldies station but nothing like what you'd consider oldies radio now days, at least in the 70's & 80's. All of the DJs had knowledge of the music and were there when these bands were playing and putting out records and they seemed to have a say in what they played, especially in the evenings when they'd take requests and dedications. Art Laboe used to do a lunch time thing in the early 80's where he'd take one act and go through the history of the artist and play tracks etc. Does the mainstream "oldies stations' even play songs like '60 Minute Man' 'Pledging My love' 'Hully Gully' 'Big Boy Pete' 'Corrido Rock' or 'Slow Down' anymore.
But growing up I think Rodney Bingenheimer on KROQ had the biggest influence on my musical tastes. When I was 14 his show was on for 4 hours each Saturday and Sunday night 8-12. Cutting his teeth in the 60's, Rodney would play stuff like Love, the Leaves, Standells, Seeds, Chocolate Watch Band, etc etc, but he'd also play the latest Black Flag demo, then the Crawdaddys, followed by the Exploited and then maybe a Crowd song right after. He'd have the Ventures or Surfaries in studio and then Frankie & Anette, then the next week X, or Blondie, or Stiv Bators. His show is just a shadow of its former self hidden away on Monday morning from 12-1am or something. Back then, even outside of Rodney's show, you'd never know what they would play next during the day. You may hear some Missing Persons song follwed by a Fear track.
Another good station here in the late 70's early 80's was KNAC before they went metal (although they did set the standard for 80's metal radio), lot's of Punk and "new music" as they called it. They'd interview bands from the Cheifs, to Rhino 39, to the Adolescents etc etc.
Then there was listener supported KPFK that had Bo Clifford on late Saturday nights playing lots of underground stuff followed by 12 O'Clock Rock with Andrea Enthal. She even had Chris D. of the Flesheaters sit in for her sometimes. He would play an amazing selection of music too.
Now today's LA Radio is pretty much irrelevant in my opinion. The only salvation is college radio . KXLU has various decent programs, but I mainly listen to Stella's show "Stray Pop" which she has been doing for damn near 30 years I think and the Reverend Dan's "Music For Nimrods" show. that follows Stray Pop, but they are on Midnight to 6 am Sunday morning, so who really get's to listen? KCSN also has a decent oldies show where you'll hear some obscure early R&B. the only thing I listen to on KPFK anymore is Rhapsody In Black where you'll here some good blues and pre-RnR Rhythm & Blues.
With all that said, it's internet radio and the podcasts here that is where it's all at for me now, though I do find myself listening to WFMU a lot now via their iPhone application.