That's a tough call. Given that you have limited time, you should stick to one area of Kyoto, certainly. The easiest to get to from the station and the one with the highest concentration of sights is Higashiyama (Eastern Kyoto) which is where Kyomizudera is. You could easily spend a few days in Higashiyama itself, but the sight-of-sights there (you know, the one in the "if this is Tuesday it must be Kyoto" bus) is Kiyomizudera, for better or worse, the Eiffel Tower of Kyoto.

If you get there early enough in the morning, and given that it is December 25th, a regular workday in Japan and not high season (high season in Kyoto is the late fall and the late spring) it may be fine. There will be some crowds, but nothing like making line at the David in Florence. It definitely is worth seeing, but it isn't going to be the atmospheric Kyoto sight some people are looking for.

If I had one day in Kyoto I would get an early start and head to the bottom of the Kyomizuzaka slope (or take a taxi to the top of the slope) visit Kyomizudera, followed by a walk around the Kiyomizuzaka, moving along the Ninenzaka into Nenenomichi, stopping to check out the stores and a temple or two along the way, and walking all the way up to the Philosopher's path. In a leisurely walk, this could very easily take you a full day if you stick to visiting 2-3 temples in detail and a leisurely lunch somewhere atmospheric.

Another, much more "secret" experience is to take a taxi to Arashiyama in Western Kyoto, and walk from the Arashiyama center up into the Sagano hills all the way into Toriimoto. Lot less crowded and quintessential Kyoto.

There are many other 1-day rounds out there, but they involve some crazy transport to some out of the way places that not even the Japanese know about.