After my extensive experience of … um… 2 months here so far, I’d echo the zoo recommendation. The night safari is way cool, but the zoo alone is fantastic - hands down the best zoo I’ve ever been to. The River Safari looks great, and is how you see the pandas - but we haven’t done that one yet, so I’m only going by research.
The Merlion is a bit meh, but probably worth a brief look and you can walk along the bay round there anyway, which is lovely.
We love Sentosa (the resorty island) but then I have two children, so we spend an awful lot of time at the water park there. The Aquarium is the biggest in the world by some measures, and it’s kind of fun. There’s also a heap of restaurants, a casino and a Universal Studios theme park there. Depending on where you’re coming from, this may be the most exciting thing in the world to you, or a bit of a smaller version of home, of course.
One of our favourite places is Marina Bay Sands - there’s a huge hotel with a boat on the roof. Well, kind of - you’ll have to see it to understand. There’s also a fantastic shopping mall pretentiously called the Shoppes - which has the sort of shops where you feel you’ve lowered the tone just by crossing the threshold. I like to look and laugh. The very coolest thing in the mall is the Venetian-style canals and gondolas, which are just random and lovely. Come out of the mall and head for the gardens and you’re in the Gardens By the Bay, which is a fabulous place and includes the Super Trees (again, you’ll have to see them to understand).
Clarke Quay and Robertson Quay are good for a wander and you can pick any of the shopping malls more at less at random for an entertaining and potentially expensive day out. Orchard Road is a sight to behold if shopping’s your thing.
I agree the Botanic Gardens is lovely. Also Fort Canning and the park surrounding it are very nice.
Taxis are plentiful and dirt cheap (compared to the UK anyway) and even the longest journey isn’t going to cost you a lot. I agree - eat eat and eat some more. We have no babysitter access yet, so I haven’t done anything really special restaurant-wise, but I’d agree that even your bog-standard chain restaurants are great here (apart from TGI Fridays - that both sucks and blows. I’m never letting my daughter pick the location again). You can spend a lot on a meal, but you can also get great food for reasonable prices.
And you do know it’s going to be hot and wet, day and night, right?