I used to go through Singapore a fair bit, and in my short few hours there, one of my favourite spots was the zoo, where I regularly go to get photographs...
Singapore Zoo is my favourite zoo, and a great place to get photographs of (seemingly) busy and happy inmates, especially the south-east Asian species.
But there are also many other animals from all over the world. There is a particular and relevant focus on tropical rainforest animals, which makes sense, as this habitat contains more than any other, and the critters feel more comfortable here than they would in a miserable and cold (in more ways than one) European zoo.
So there is a good focus on primates: tamarins, gibbons, macaques, spider monkey, capuchin, apes, proboscis monkey, etc.
And being a zoo in a well developed tropical country means there is a lot of local wildlife walking around...
It takes about half an hour from the city to the zoo via a taxi, and this is usually a Singapore$30 fare, depending on traffic. The entry fee is S$33 (2016 prices).
Another wildlife park in Singapore is Jurong Bird Park