Some questions
What day of the week (this may influence local food and island visits)? Do you like walking (in humid climate) or "nature"? Do you want to go swimming (if visiting islands?)
Islands are OK for filling in time, it's actually quite nice to go for a swim on Lazarus Island, which you can do by catching the ferry to St John's Island and walking across a causeway. Schedules
here, more flexibility (and busier) on weekends. No food or drink available on the islands, so you need to take with you. Full disclosure: locals are a little worried about sea lice, I've swum there twice, first time I had one red dot that may have been sea lice or something, the other time nothing. Nice enough to visit even if not swimming, if you have nothing better to do.
For some pleasant walks , can do a 11km boardwalk/rainforest walk around MacRitchie Reservoir, with a detour for a canopy walk, google for information. For a view, the Southern Ridges walk, which starts at Mt Faber, near Sentosa/Vivo City and walks along the hilltops across Henderson Waves and a treetops walk structure through to Hort Park and Kent Ridge, where you can catch MRT back. Both walks take about 2-3 hours. Alternatively, there's some nature walks if you are into birds, lizards and swampy things (sometimes see crocs) at Sungei Buloh wetlands, but it is a long way (in Singapore terms) from the centre, towards the north west end of the island, near Kranji.
For a lazier day, if you have an interest in planes, and if they are landing from the north, pleasant to head to Changi Village, tuck into some BBQ Chicken wings and whatever else takes your fancy at the hawker stall, then go for a stroll down to Changi Beach, get a great view of the planes coming into land (if landing from south, taking off to the north, departing planes aren't quite so close). Otherwise, can head to East Coast Lagoon, mid afternoon for chicken wings, satay and seafood and then you can wander along the beach (?!) a bit as well, can also be a pleasant way to spend an afternoon (but not really before 2pm).
I am sure others have plenty of suggestions too. You might want to get a visitors point of view for food. I have my favourites, but have been here now for almost eight years so this invariably means that at one hawker centre/food court I only like Dish A, for Dish B I have to go to a different one, Dish C another again ..... OMG getting way to fussy....
