We just came back from Singapore 2 days ago. Rasa Sentose is a bit far from the city. However, Singapore is a pretty small city, and it's OK to stay there and travel downtown. I don't know how you go to legoland as it's in Malaysia.
We stayed 2 nights at Festive hotel on Sentosa Island and 3 nights at Fullerton downtown. 1 full day at Universal studio is enough, and you may want to spend 1-2 days at Sentosa Island as there are plenty of indoor and outdoor activities there. We rode Luge and Segway, and lots of fun for my 8-year-old kid. We also tried iFly which was a great experience for my whole family. We spent 1 whole day at wild wild wet too.