As everyone else has said, cable car over to Sentosa, do the southern ridges walk to get there too, very nice.
Night safari is excellent, do it once on foot and once in the "train" as the train goes a different route and you see different things.
Visit a hawker stall: Lau Pa Sat is the big tourist one, but nearby Newton food centre is more "proper" Whilst you're in Chinatown visit the buddah tooth temple but find the elevators and go up a few floors it's way less busy and still spectacular
Long bar at Raffles for the Monkey nuts
Gardens by the bay. The giant greenhouses are amazing especially the larger sky forest one.
Fort Canning if you can cope with hills in the searing heat
If you want some nice real Singaporean food that isn't a hawker centre but isn't crazy expensive (for Singapore standards) one of the National kitchen by Violet Oon is worth a look.
Atlas bar for really poncey cocktails in a spectacular setting
Kampang Glan for a look at what old Singapore might have been like with it's tonne of shophouses, and pretty mosque
For authentic Singaporean breakfast go to a toastbox, but be prepared to queue, it's where the locals eat out
For something a bit more "benidorm" a night at Clarke quay.
Unlike the others I'm not sure I can recommend ce la vie at the top of Marina Bay Sands. Yes the view is spectacular but the drinks are poor and the prices are silly.
If you have time on the flight home the jewel at Changi is worth a a visit BUT as with much of Singapore the experience depends on how much cash you spend. If you don't be tickets to any of the access areas it's basically the metro centre with departure boards. If you spend to go on the attractions they are pricey but give you the best views and places, there's a nice chill cafe at the top that's great for a pre flight relax.
Singapore seems to be a re Marmite kind of place. I love it, in actual fact wanted to move there before I was married but to some it's essentially a giant, sweaty shopping mall in a jungle.
And of course, as obliquely mentioned above, if you're of the mind to, visit Orchard Place, AKA "The four floors of wh****" (Don't do this!)