Been a while since i was last there but try Sembawang area, there may still be some old world stores out of the way that have had odd stock in boxes out back for years, they where always far cheaper than any plaza.Also some cool old buildings out this way. Kranji memorial, dunno, all depends on what you are looking for , Singapore on the surface can seem a little sterile, walkabout and you can be surprised.
Consider a bus over the causeway to Jahore Bahru.