SIM cards and data packages throughout Southeast Asia are affordable, even in expensive Singapore, although perhaps not as affordable as other Southeast Asian countries.
Even though there is free WIFI in the touristy areas and almost all malls, it is not something you want to rely on. Speeds may be deplorable, the hotspot may not work, and you are putting your traffic at risk.
Get yourself a Singaporean SIM card – you will thank yourself. Click on any of the logos to read my review of the said operator, or you could read my Best Prepaid SIM Card in Singapore Comparison, where I compare everything I know about Singtel, StarHub, and M1, and see which operator is the best for certain scenarios.