Try Holland Village, especially on Friday and Saturday evenings. It's a food enclave complete with bars and restaurants. At night, the roads are closed, so there's quite abit of nightlife there. Because of the proximity to the universities, and it being located in the west, which is the "place to be" area right now, the crowds are younger, are less pretentious and the mood is more laidback. Many Singaporeans who get tatoos get it at Holland Shopping Centre.
If you like futuristic architecture, then you should visit the one-North area comprising of Biopolis and Fusionopolis. The skyline here is reminiscent of those "city in the future" scenes you see in Hollywood movies. Just a stone throw away is Portsdown Road and Rochester, restaurants located in colonial bungalows... it's really rustic and very nice to get a drink or hang out.
If you fancy a swim, and don't want to pay more than $2, then head down to Jurong East Swimming Complex. Complete with a wave pool, 5-storey slide tunnels a looping river for you to rest and relax as it takes you round the complex, or just a normal swim - it's a good place to get a tan or just get away from the heat.
Want to know a close and personal visit of The Matrix's Machine City? Machine City's fake but hop onto a bus bound for the industrial estates like Benoi and Gul to experience towering industrial and metal structures, or see container ships in their last stages of construction at the dry dock as you are taken around the area.
Lastly, the Chinese and Japanese Gardens. During Mid-Autumn Festival, Chinese Garden is transformed into a amusement park complete with huge light and lantern structures... kinda like Harbin's Ice City but without the ice.