The combination is 7 23 30 and is found behind the counter when you have to rescue Artie. Play through the game like normal until you see the cutscene where Tannen leaves the speakeasy through the secret passage. After you see Tannen use the passage, go to the roulette table and an option comes up which allows you to put in the combination you found earlier. Use it and the door opens up.
I can't get any more specific than that.
Originally Posted by RexMaster
I love this guy! There is nothing more to it!
"I hope you know what you're doing, Doc..."
"When I was older, I loved experimenting with time machines."