I live on the west side (LA) and my local rinks are culver (culver ice arena) and el segundo (healthsouth iceplex). health south has much larger rinks and culver has one medium size rink. But the ice is so much better at culver and i like the atmosphere better. i would suggest u deside which rink to go to then pick a coach. ask the skating school. at culver, Gina Testa is great with kids and shes a good coach up untill axle/double salcow jumps. Then Gary or Arlene are wonderful. They are great with kids, and teach eight yr-olds axels, but i dont know if they teach the stroking level. Hope this helps.
[PS. just in case ur not on the west side, i think that the rinks downtown and at universal dont have schools. check out the van nays one, or the pasadena one.]