Alas, all the beaches in easy striking distance of Singapore -- which basically means Desaru, Bintan, Batam, and Sentosa -- kind of suck, the water just isn't clean. The northern Bintan hotel bubble is the least bad facilitywise, but if all you want is a pool and cocktails, you might be better off staying at one of the resortier hotels in Singapore itself.
The other option is to fly somewhere that does have great beaches: Phuket, Langkawi and Koh Samui are all around 1.5 hours away by plane.