Follows are just the places I have tried before,
1). Holland Road, There are two bars in Holland road. They are all quite ok, not so expensive. 1 Beer is about 7-8 dollars depends on the brand. Vodka is also quite good, my experience is Vodka Orange, Vodka 7-up. The red wine is not so good at least the House Made Red Wine is really bad.
2). Tanglin Shopping Center. The place is at the back of the Tanglin Shopping Center. I tried Tiger Beer there, it is about 26 per "Ja" (= 5 cup). The place has a good environment much better than Holland Road. It has a Garden in the back of that bar, you could drink in the Garden and it is completely no light at night. So no one can see each other... :)...
3). There are two bars in Far East Square (near raffles MRT). These two bars are quite good bars, the drink is a little expensive but the environment is Good. The name of the bars are "Cooles" and "Carnegie". Carnegie will have free buffee every wednesday with drinks.
4). Some other Hotels, like Swiss-Hotel, Fullerton. I like Fullerton, there is a bar in the first level of Fullerton Hotel. The drink price is not so expensive, like 1 Stella Beer 7 and Vodka is 15-20. There is an inside small room with funny tables and chairs. You could hide youself there and drink. :)
5). Outside the One-Fullerton, quite normal place, but near the sea.
6). The cheapest way to drink is to buy beers in NTUC and drink in your own room. :).