Sentosa - especially catch the fountain show
National Museum - if you have time, can add Asian Civilization
Museum
Zoo - the daytime zoo, it has more shows
Esplanade - schedule your arrival to watch a few shows
Big Wheel - enter it
Singapore river/ clarke quay boat tour - nighttime is better,
very scenic
Orchard rd - sightseeing
Discovery centre and science centre - always good for all ages,
catch the 3D show
Food centres - such as food courts inside malls, choose a place
with wide selection and variety of local food. Tourists especially
like this.
Beaches/ Parks - sightseeing, sunset-watching, roller-blading,
or cycling, strolling/ chit-chatting
Downtown East - go to the themepark, the land one or the water
one
Kallang Entertainment Centre - ice skating, also have bowling
and other things.
Libraries - good collection of books
Thats all from me, enjoy.
* I add one more: underwater world.