1) Singapore Flyer
2) If you like animals, then Jurong bird park, Singapore Zoo + Night Safari
3) Eat at the local hawker center. I recommend a good chilly crab. Be prepared to cry when chilli hits your ass

4) Checkout some unknown tourist spots like, Singapore Discovery center.
5) Visit Singapore art museum (if you like art of course)
6) Hop on the city tour bus at Suntec city (Mall), just go around the city. If flying on Singapore airlines, then hop on bus is free.
7) Go clubbing at clarke quay, Pick up some chinese or malay girls
8) Find out ways to open a singapore bank account to save taxes in future

9) I strongly suggest if you want to explore the city, take the public transport. Even when you can afford a taxi. MRT and bus services are just excellent here, Way above the world's standards.
10) Don't fuck around in the public places, jaywalking or throwing rubbish, Our city is cleaner than the white house.
11) Sentosa beach and universal studios (Avoid weekends)