-> Go for one of the champagne brunches, preferably in Fullerton (the building is interesting)
-> Visit Equinox or nearby bar and see Singapore from the high floor (spectacular view)
-> Visit Orchard Towers during weekend (local scene for party animals)
-> eat in hawker centres, best are in the suburbs (so you can get good food and other attractions like old lady selling 4D lottery tickets, old guy holding a type of nose inhalator in his nostril etc.)
-> take a ride in a MRT i. e., towards Woodlands (to see people sleeping, clipping their fingernails and all the rest of local peculiarities
-> Go to Pulau Ubin (rent a bike and chase chickens around the island
-> visit Singapore Botanical Gardens and orchid garden (beautiful flowers and other plants like pineapples, ginger etc.)
-> go to Chinatown around Chinese New Year (be prepared for the crowd)
-> attend local weddings (each culture has own celebrations, but it is all so interesting and worth seeing)
-> talk with locals about the cultural differences (you must know them a little, so they could be honest or react spontaneously)
-> visit one of the spas for the massage (foot massage is also good)
-> visit Mustafa mall
at least once (to see everything under one roof)
-> go to Esplanade for a concert
-> participate in one of the dance and dinners organized by your employer (specific food, different 'attractions' like silly lucky draws or competitions)