Pickwick is probably your easiest good option. Valley Ice Center is also close and maybe not as busy. The closest rink would be Van Nuys, but it's small and dark.
Toyota Center in El Segundo is a really nice facility with lots of ice time (3 surfaces) and not far from where you are staying. Unfortunately the 405 freeway is undergoing construction and the traffic is usually bad going over the pass from the valley. However, if it were me I would definitely go and skate there with the added bonus of watching whoever was training with Frank Carroll. EastWest in Artesia is another good option for skating alongside or just watching high level and elite skaters.
There are many other rinks as well and they all have public and freestyle schedules on the web. If you want more info, please feel free to PM me. Have fun!