Race Course Rd has some funky pubs and bars. Desker Road is Singapore's dingiest quarter of ill repute and best avoided, especially on Sundays.
Little India has quite a few sarabat stalls offering local drinks, especially teh tarik "pulled tea", a Malaysian variant of sweet, milky Indian chai, also available in iced. A particularly popular one can be found at the intersection of Perak and Dunlop Rds, next to the mosque.
Prince of Wales Backpacker Pub
101 Dunlop St
+65-62990130
Brightly painted Australian corner pub/hostel transplanted in Singapore, with Gippsland Gold draught beer shipped in, near-nightly live music and fun theme nights eg. free drinks for guys in skirts. Drinks around S$10 half price for in-house guests, dorms S$18, Private rooms with windows & private bathroom S$60 aircon.