Hi,
if you are really into a relaxing & romantic time away from it all, can try Changi Village hotel. Tried it on a public holiday, service tiptop.
Executive floor, only 600plus for 3 nights. Worth every penny.
Free drinks in the fridge that will be refilled every day!
May have cheaper rooms there maybe you can call and check.
We went Pulau Ubin for a day, the beach next and 3rd day "relaxing" in the room.
goodluck!