There are a whole host of art venues and heritage museums that display the best and latest modern and historical shows as well as displaying some of the regions best in historical art pieces and exhibitions to boggle the mind. Both an educational and awe inspiring experience, I highly recommend a visit to the Arts Civilisation Museum or even the National Musuem of Singapore - to the greatest shows of the month. Rounding off the trip with a good local meal at any one of the shophouses to complete your cultural experience.
You can hit the beach, at Singapore's very own Sentosa or 'tranquility' beach located off the main island. Also you can partake in activities like go-carting, the mini-luge at Sentosa, the famous Reception cable car or even a ride on currently the world's biggest ferris wheel located just off of Marina bay - in a location just minutes from where the first F1 Grand Prix night race took place.
There are so many things for you to do in Singapore and no visitor's guide is merely sufficient in spelling out the things you can discover and the things you can do. The best guide you can ever get is a local - he or she (depending on your orientation) will be able to give you the best sounds, the best sights and the best tastes that this country has to offer.