Mint Museum of Toys behind Raffles Hotel
Get some custom tailoring done to suit your own design aesthetic
Cheap eyewear for sale, if you already have a prescription
Check out HDB housing as suggested. Hit a wet market/hawker center to see how locals shop & eat. Bukit Merah View is very "local." However, Peoples' Park Eating Centre in Chinatown has much better food and food selection
Find a local drink stand in a local hawker center and ask the "uncles" loitering about to recommend favorite foods. Sure to get a lively discussion started.