The city of Singapore is actually very small you could probably tour the entire city in a matter of just a few days.
You can tour the city in a short time but to appreciate the history and culture and diversity you will need much long.
Singapore still has a strong air of British colonialism. The Colonial Core as it is called famous for its beautiful architecture including the rebuilt government building churches and cathedrals. Singapore cricket club also locate their. In 1819 this with a Sports Center for the British colonist. There also many museums in and around this district including the Singapore Art Museum.
While in Singapore you won't want to miss its famous shopping district Orchard Road this is probably the most famous shopping area on the island. There is also a great Chinatown here where you could discover Chinese culture and history. Also India is well represented on the island visit Little India for a unique experience. There are so many different nationalities that can be explored on this exotic island. Check with your travel agent for all the numerous tours and hotels to stay at in this unique country.