Well, I can personally attest to the fact that Ken Shelley and JoJo Starbuck, and Tai & Randy started skating at the now deceased Ice Capades Chalet in Santa Monica (I was there in the early 70s taking lessons as well, but to no avail). Debi Thomas's training ground was the Culver City ice rink (which is still going strong). Michelle Kwan got her start at The Olympic Ice Arena (which is now called The Skating Edge) on Western Ave. at the border of Torrance and Harbor City. I believe that Sasha Cohen, Naomi Nari Nam, the Stieglers and Angela Nikodinov are all alumni of the Skate Zone in Huntington Beach.
Nowadays, everyone (Timothy Goebel, Amber Corwin, Yebin Mok, Danielle Kahle etc.) seems to be training at the new Iceoplex chains that suddenly started springing up like weeds at the turn of the century in places like West Hills, Panorama City, El Segundo, and Escondido.
As you can see, there is a literal glutton of rinks in the Los Angeles area, but that's to be expected in a city with a population of 10,000,000. I don't know anything about skaters who aren't from Sourthern California