Old fashioned soda fountain on the Westside
Only places that come to mind are:
11623 Santa Monica Blvd
Los Angeles, CA 90025-2907
310 479 1955
and Johnny Rockets
You didn't mention anything about food so maybe the above two are safe bets for what you want.
Now for a real authentic old time soda fountain you'd have to go to Fair Oaks Pharmacy in S. Pasadena and for a pretty top notch selection of shakes and flavored sodas it would be Connal's in Pasadena.