Singapore is a very tourist-friendly country. Just book that flight, get a vicinity map at the airport, and crawl the city. The moment you leave the airport going to the city, you will embrace their efficient train system.
This is a different Singapore trip since I intently attended ZoukOut 2014, a dance music fest of Zouk.
What I Did?
Afternoon: Arrival in Singapore
Night: ZoukOut (Sentosa)
Morning: Chinatown, Hawkers
Lunch to Night: Marina Bay Sands (Mall, Helix Bridge, Man-Made Lake, Art-Science Museum, Merlion, Singapore Eye)
Night: Bus Ride to KL
The Marina area is a big complex where you can devote a whole day touring it.