Don't know which of these might have Asian LPs, but give a call:
Counterpoint on Franklin (best bet for classical)
East Side on Hillhurst
Amoeba on Sunset
Record Surplus on Pico
Record Recycler on (moved from Hollywood, but it's somewhere)
Rockaway in Silverlake
Bagatelle in Long Beach
Atomic in Burbank
Murray's The Record Man (?name) somewhere central
That should be enough to start with - LA is the BEST vinyl shopping city in the US.
Patrick