I think I am the best person to reply you as I am a Singaporean who previously work in Taipei, visit Hong Kong for holiday and currently reside in Singapore
Hong Kong is give you more vibrant as compare to Singapore. Singapore give you the `wow` as a cleanliness, order, neat and well-design building/roads.
Places to visit in Singapore include Sentosa, Orchard Road (Similiar to Taipei Zhongxiao Sogo), Bugis Junction (Similiar to Taipei Ximenting), Geylang (For its local food and infamous Red Light District), Clark Quay/Boat Quay for riverside dining and drinks, Esplanade/Singapore River/Fullerton One for night view and dining.
Shopping places are Orchard Road, Suntec City, Bugies Junction, City Link/Raffles Places and Chinatown
Latest hot clubbing place includes Club Momo (Robertson Quay), Liquid Room playing trance music with lots of expatriate (United Square), Thumpers playing 80s retro (ORchard Road Goodwood Park), Devils Bar and AsiaBar. Mohammed Sultan used to be a hot Singapore own Ropponggi but it is now a dead town.
Try to get a Local to bring you around either in Hong Kong or Singapore.