Try Beer Garden at St James Power Station. Nearest MRT station is Harbourfront.
Outdoor dining area. Good bands on occasion.
There’s Timbre @ Substation. Nearest MRT (City Hall).
Else, a little off the main tourist spots is the River Valley district. Popular hangouts along Mohamed Sultan Road or Robertson Quay. Still pricey. There’s Wine Bar at Zouk – a popular club – (Jiak Kim Street) which have some cheap deals.
Finally another good district is Duxton Hill area (Nearest MRT at Tanjong Pagar)
Other options are further away from the main city area.
Let me know if you’re interested in those.