Don't worry, for Santa Fe you are not getting an early jump
Book now if you want to stay close to the plaza. Otherwise motel row on Cerrillos.
What is your budget ? The closer to the plaza the more expensive. B&Bs are nice, but pricy.
Traffic can be bad, but not as bad as Taos usually. Parking near the plaza is the main issue.
There may be enough snow for a trip up to the public ski area outside of town. They have some black runs if they have had enough early snow. Otherwise mostly greens. Taos is only a few hours drive north otherwise.
In town, lots of architecture, Georgia O'Keefe museum, history and culture museum, several famous churches, lots of tourist shopping, etc. the SW art colony scene.
Outside of town, there is the Gorge of the Rio Grande and bridge, Pueblos ( fee for photos) , the national forest (Santa Fe National forest) is due east. There is a very scenic drive called the Old High Road into Santa Fee that is worth exploring for the churches and scenery. Bandelier National Monument is nearby (next to Los Alamos) and worth exploring.
The weather can turn rapidly that time of year. i have been snowed in twice the last two trips between Christmas and New Years. It was a couple days before we could move. Front wheel drive is generally good enough, unless you want to be the first out. If you go up in the national forest, i would carry chains and/or 4wd.