Even in the slower months you'll want to book your attractions in advance - sometimes it can save you queuing too (great in the cold!)
All over the city you'll find festive markets and decorations - this is Covent Garden right in the center.
With shorter days and potential bad weather, having your hotel or apartment in the center of the city is a great idea. At least be close to a tube station!
With early sunsets you might find that you have time on your hands in the evening with nothing to do! The west end theatres are a great place to look for a fun evening.