Ours loved the Cappella pool villas because of the plunge pool and outdoor shower, every night she had room service of choco cookies and milk in bed. If you have an HSBC credit card they are doing a good deal with points.
All decent hotels will do a birthday treat, cakes etc.
Again its very much up to what the kid likes, does she/he like the beach, roller coaster rides, playgrounds, boats, horses, tree climbing adventures, kids shows, clowns, swimming/water parks, biking, ice skating, snow and ice, cable car rides, prawn fishing and BBQ etc there a shed load of stuff for kids/eating joints in Singapore.
How about a picnic in Bot gardens the verde cafe does a two for one specials pizza mid week, take the Frisbee, scooter etc. do the dinosaur walk first.
Other good one is the pan pacific outdoor restaurant, has a playground next to it and the kids loves the glass lift rides "Say its a rocket"
Camping/picnic? at Sentosa, walking distance from tanjong beach club so you can stock up on drinks and food.