If you want to experience it the way the working class locals do, go to one of the popular outdoor coffee shops that play the game. A great one to try would be one of the ones on Geylang Rd, say at Lorong 12, as that area is quite lively at all hours of the night. There are some threads here from people posting and complaining about the noise coming from the area at 3am
For a Westerner Expat experience, one of the bars at Boat Quay. I'm not sure which ones will be open or playing it, but if you go there and ask they'll tell you (or already have schedules posted). OT might be another good choice if you're single.