You'll be in pool heaven
There are lots of great options for pool all over Singapore. My main place was the previously mentioned Klassic Club. It's in Little India, is a locals room, 18 pool tables, a dozen snooker tables. SG$10 for 3-5 hours depending on the time of the day. That's per table, not per person. Aloysius Yapp plays there.
Next up would be Brunswick Billiards at The Cathay on Orchard road. Go there on Saturday at noon. There's a group that meets up every week and occasionally has a tournament. Lots of social players there, but also a lot of the upper level amateurs that I played with most of the time. Go there and ask for Kyoko, tell her Burt sent you and have her introduce you to Evan, Dylan, Jason, or Ethan. They play most weekends and often in the evenings. Also poker fans if you're into that. Brunswick is expensive to play by the hour SG$20, but the group meetup is usually about SG$8 for 3 hours.
There's a place in Toa Payoh on the top floor above the McDonalds near the Library. Close to MRT station, some really good players there, smaller and often crowded. SG$10 for 2 hours from 12-2 on weekends and more reasonable hourly rates otherwise. Tournaments often.
After that, Punggol Billiards. About 10 minute walk from MRT station. Big room, not as busy, only went a couple times. Hard to get to without a car so unless you're living nearby not the most popular choice.
Close to MRT station, some really good players there, smaller and often crowded. SG$10 for 2 hours from 12-2 on weekends and more reasonable hourly rates otherwise.
Honestly though, if you go to The Cathay on a Saturday and meet the people I told you about, you'll be all set. They're good guys. You'll enjoy living in Singapore, I spent 2.5 years there and came back last year. Don't be shy with the local food, it's great, try everything. Anything else just ask.