Shop at Haji Lane
Dinner at Blu Jazz (Funky and Relaxed Jazz Bar with indoors and outdoors)
Then have a drink at the amazing batman like art deco building across the road called Parkview, live music some nights
Walk at Fort Canning Park - the historical birthplace of Singapore, also check out the spice garden with real cocao trees, cinnamon trees, banana palms and other delicacies (Hotel Fort Kanning is great too and in walking distance to most central places.
Lunch or Dinner at Lewin Terrace, amazing food and wonderful black/white house, the old firestation's chief villa (use the back door directly from the park)
Then have a drink (night) at the Timbre @ substation - rock and roll!
Visit National Design Centre: Design and Maker Studio (very innovative stuff).
Visit the Singapore Art Museum (SAM
Also, check out Lasalle Art School and Sota for their architecture.
Have lunch at Open Farm Community
and a coffee at Tiong Bahru Bakery
Also! Any local Hawker Centre - a must must must!
Dinner at Din Tai Fung (try the dim sum with black truffle, yummy!)