Singapore is awesome, I used to live there and my dad's side of the family is from there. Can't help much with nightlife but I do have general tips.
The food in Singapore is amazing... Eat lots! There's this guidebook called the Makan Sutra which is very handy and useful. Check out the Marina Bay area. Hawker centres are cheap and so good. Watch the Anthony Bourdain episodes on Singapore for good tips. You can go crazy expensive or cheap but delicious. I miss the food so bad.
The Gardens by the Bay are pretty cool, so is the Singapore Flyer. Go up to Ku De Ta at the Marina Bay Sands and have a drink at the Sky Terrace without having to pay for a ticket. Go to the 'Durian' aka the Esplanade Theatre. Go to the Singapore Botanical Gardens. Go to Jurong Bird Park and have lunch with the birds. Lots of very interesting museums as well. Sentosa Island is touristy but fun. East Coast Park is interesting, worth a morning stroll if you have time.
Orchard Road for the endless line of shopping malls. Go get lost at Mustafa Centre, it's huge. ION Orchard, Tanglin Place for all your high end shopping needs. So many to choose from haha.
There's lots of history in Singapore too. Check out Little India and Little China. Clarke Quay is amazing at night. Go to Fort Canning, which has been converted from a military base to shops and restaurants. The Raffles Hotel is interesting to visit, and is the birthplace of the Singapore Sling. Pulau Ubin is worth a day trip, it's like an old school village only a 15 minute boat ride away from a bustling metropolis. Like going back in time to Singapore in the 1950's.
Two weeks is a lot of time in Singapore. You could book a cheap ticket to Bali for a few days and have fun there too. Or take day trips to Johor Bahru in Malaysia.