Christmas Day is an official public holilday in Singapore so I'm not sure about everything being open. As far as hotels go my recommendation is the Raffles Plaza right next to the famous Raffles on Bras Basah Rd. It's not overly corporate and stuffy, has very well thought-out rooms and the most amazingly beatutiful bathrooms. It's also conveniently located above Raffles City Shopping Centre and Raffles MRT, about three stops from Orchard Rd.