People Park Centre. The old shops you find upstair of the food centre. Those shops that sells rolls of fabric...some of them would sell buttons as well if not exclusively. From the normal type you find for basic white shirt to the more colour cooridnated colour buttons to some of those fancy fabric covered ones as well.
In town you can try that large store called "spotlight" ( I think ) found at Plaza Singapura. 3rd or 4th floor I think. They sell alot of arts and craft stuff plus alot of sewing/knitting stuff. Saw they have alot of various buttons there too. Was there just last week searching for some stuff.
For basis white shirt buttons, think it is easily found in any housing estate.