For rentals, I recommend
www.craigslist.org (Los Angeles section).
Areas that seem to be more dog friendly:
South Bay (Redondo Beach, Manhattan Beach, Hermosa Beach)
Long Beach
Marina Del Rey
Santa Monica
Venice
Torrance
South Pasadena
Pasadena
I would definitely use craigslist,...as this is how my girlfriend and I found our current place. Also...Santa Monica/Venice is a great place to look because of rent control. I just recently moved from Redondo Beach to South Pasadena (I miss the beach!).
And as SoCalyorkiLvr mentioned...definitely read the "No Dogs Allowed" thread (specifically the 2nd page).
http://www.yorkietalk.com/forums/sho...8&page=2&pp=15
This 2nd thread entitled "Where do you go" offers some similar and good info as well.
http://yorkietalk.com/forums/showthr...ht=service+dog