Well, unfortunately you'll be arriving on a Sunday, otherwise I would recommend the big Chatuchak weekend market for shopping, but maybe you can make that on your way home.
If you are completely blank about where to go you should know that visiting the Grand Palace, temple of the Emerald Buddha, is an absolute must for Bangkok visitors!
My advise about New Year would be to avoid the big crowds in the center of Bangkok. There might be too much trouble.
Four days in Bangkok should be plenty to experience the metropol. After that a place of interest might be at least two days in a nice and quiet provincial city like Kanchanaburi two hours (125 km) west of Bangkok. It's the city with the historic places like the Bridge on the River Kwai, the War Cemetary with 7000 headstones of allied soldiers who died during the building of the Death Railway and the Hellfire Pass in World War II. Take a small trip on the railway and enjoy the beautiful landscapes along the river, and enjoy a good and cheap meal at one of the many restaurants by or on the riverside promenade, and make a good bargain at the evening market by the train station.