Great Christmas present! First off, how much are you willing to spend? They start at about $30 and go up to more than $400. If this is her first HRM, I would suggest a lower-end model that's easy to use. Acumen makes one for about $40 and it's designed for women (Eon Basix ES WP Womens Heart Rate Monitor for Smaller Wrists), so the watch is quite small. I was very happy with mine (at least until I cracked it rock climbing and subsequently water logged it swimming).
If you're willing to spend a bit more, my recommendation would be the Polar F6, which retails for about $100. Like the Acumen, it gives you a reading for your actual heart rate, but it also gives you a reading for the percentage of your heart-rate maximum, which is useful to know. Also, the Polar F6 records your workouts, so you can go back and see how many calories you burned, over how long a period, etc. FYI, Polar is the best-known maker of HRMs, but they also tend to make more expensive models -- Timex, as the previous poster notes, makes cheaper models, as does Nike. Amazon is actually a good place to see the various available models -- more so than most sports equipment web sites, actually -- although obviously you can't look at and play with them online.
If money is no object, you can consider looking at some of the more advanced (and specialized) models like the Polar 625X (with a foot pod for runners/triathletes) or the 725X (with a bike mount for cyclists/triathletes), the Garmin Forerunner 305 (for runners, with GPS) or Suunto also makes some good ones. (I'm not as familiar with those models, but when I was at the HRM counter at Paragon Sports, two guys in a row -- runners, both -- came in for Suuntos).
One issue you will want to consider is whether the HRM is coded or not. Coding means that the watch will only pick up the signal from one transmitter. This is important if your daughter is working out indoors -- like in a spinning class -- where other people have HRMs. If her model is not coded, the watch won't give an accurate reading. Coded models aren't that much more expensive -- and I believe all newer models are coded -- so it's worth it to shell out the extra cash.
Another issue to keep in mind -- and you/your daughter may already know this -- but you need to know how to properly set and use a heart-rate monitor to really benefit from it. Readings have to be interpreted properly and your daughter should know what her aerobic vs. anaerobic zone is, etc. A lot of this information will be in the manual, and this site and others have a lot of information about how to use HRMs.
Somewhere in the world someone is training when you are not. When you race him, he will win.