There used to be (and I am guessing there till is) a day bus trip to Malaysia to visit parts of Johor Bahru, a rubber plantation and a fishing village, with a stop for lunch at the fishing village. You might run a search here, or ask at your hotel. You see part of the Royal Palace in Johur and some markets as well as the fishing village out on stilts over the water. A little touristy, but fun.

A good overnight trip would be Malacca/Meleka, which has a lot of old Portuguese colonial buildings and an old Chinese town as well. You can take a bus or drive yourself by renting a car either in Singapore or just over the causeway in Johor Bahru. The drive takes about 3 hours, and there are places to stop to buy china along the way. Haven't been in a few years, but there is a Renaissance hotel there which was nice. You could easily book this over the net or ask your hotel in Singapore to arrange. You might want to search for other more traditional Malay/Chinese hotels, people on this site may have suggestions or run a search here.

Some people like to go to Bintan island for a day or overnight, I don't think the beaches are very nice, but it?s a personal thing. Your hotel could give you information, or run a search on the internet.

If the weather is nice, there are parts of Singapore which you can go to which will make you feel like you have gotten away from the city. There is a windsurfing area in Singapore's East Coast area with a nice beach where you can rent lasers and windsurfers and have lunch or dinner. Pasta Fresca Seasports Centre, 1212 East Coast Parkway, Singapore. Tel 65-4495118 (formerly the Europa Windsurfing Club). You can also rent bikes and ride along the bike paths in the park on the East Coast.

You can also rent sailboats in the marina near Changi airport.

If you like to waterski or wakeboard, there is an official place for this where international competitions are held. (Welcome to Singapore!) Take a look at http://www.extreme.com.sg/

You can also waterski in the Ponggol Point area of Singapore, about a 20 minute cab ride, you can also get there by public bus in just over an hour or so. The skiing is on Selator island, in the waterway between Malaysia and Singapore. You will definitely feel like you have left the city behind. Take a look at http://www.williamwatersports.com.sg/. I am personally familiar with this operator, and would highly recommend them. There are some great seafood restaurants here as well.

Although I am not a big fan of Sentosa Island (an ersatz Disneyland IMO, but not nearly as interesting or well-organized as the real thing) there is a great hotel on the island which is good for a day trip or overnight. The hotel is the Sentosa Resort & Spa, take a look at http://www.thesentosa.com. There are pretty views of the sea and island, a nice black pool, a spa and some good restaurants. (The hotel is run by Beaufort resorts.) There is also a Shangri-La there, which I don't know much about, take a look at http://www.shangri-la.com/eng/index.htm. The island is really about 30 feet off of Singapore, you can take a taxi or a bus from downtown Singapore in about 15 minutes.

December is not a great time of year for the beaches of the east coast like Kuantan and Tioman Island, as it is the middle of the rainy season. You could probably take a day high-speed catamaran trip to Tioman, but you would probably find the waters rougher than you would like.