My male friends are all very happy with Oxford Tailor, their shop is on the 4th floor of OUB Centre, Raffles Place. Their owners (Alex and Diana) are Singaporeans and the quality of their workmanship and fabric is much, much better than at all the Indian-run tailor shops near Orchard Road that cater mostly to tourists.
Expect to pay around S$500-600 for a suit in the best fabric quality they have (120 or 130 thread), and between S$60-100 for a shirt.