The Tinder Box is the oldest tobacconist in Los Angeles.
They have no web-presence and I give these details:
2729 Wilshire Blvd
Santa Monica, CA 90403-4795
While I haven't seen Arnold buying his cigars there, there are pictures on the walls of many celebrities, from Bing Crosby to Bill Cosby. If you were wondering, The Hollywood Rounder smokes their Continental blend of pipe tobacco.
All photos on the Rounder's pages can be enlarged by clicking them.