There're many supermarkets and provision shops dotting the town. Those seem to be for dry goods and household products. For meat, vegetables and raw items to be cooked, those are separately found at either little stalls along the road set up by enterprising owners or convened at the bigger 'wet markets'.
Go early to catch all the sights and sounds. People shop early at the wet markets anyway. At home, I pop in to Tekka and Tiong Bahru Market all the time, and once in a while, if I feel like braving the crowds, Empress Place Wet Market and Bukit Timah Wet Market offer a break from the routine. There aren't cooked food stalls inside the Zhongdian wet markets though. But they line the streets surrounding it. If you like local breakfasts, especially dough fritters and soya milk (豆浆油条), you'll find plenty of such offerings at random stalls.
It's not that fun strolling along the stalls with nothing to buy. The best way to familiarize yourself with the wet markets is to head out with the a-yis and watch them shop for the day's meals. The a-yis like to pop in to the markets on a daily basis, or every other day. They don't particularly like using the fridge very much. It's like...it's cold enough here, and the fridge is like an expensive necessity that they would not use unless the summer is hot. People chill bottled drinks in the streams and rivers anyway.
The excitement, bustle, smells and colors. Freshly butchered slabs of meats laid out plump, bloody and bright. Vegetables plucked in the wee hours of the morning still hold soil and mud are merrily stacked in baskets for us to buy by the kilograms. Here, people shop in bulk and not by a quarter of a chicken or whatever. You get your money's worth when you buy the whole chicken or the whole hind leg of the yak or something. Nothing looks very fake here. They're all sourced from the surrounding farmlands that have produced rich and fertile harvests this year.