Though it is likely to be bitingly cold. Keep warm with frequent hot chocolates or gluhwein (sp?) from the Christmas market in the old town square. There is also a large market in Wenceslas Square, but although it is undoubtedly historic the Square (really a long street) is fairly charmless.

I would stick to the old town, though you can really see most of the sites in the city on foot in a morning or afternoon, saving the other part of the day for the Castle. Make sure to walk across Charles Bridge at dawn or dusk; if it is misty the statues are wonderfully atmospheric.

On the other side of the road from the Opera House, which is all art deco and 30s fittings, nice for lunch. And there's the mini Eifel Tower just up the hill from the Castle.

is worth an hour or so if that's your sort of thing. Not glamorous but quite central. There is a shop next door selling reproduction Cubist designs made to a high standard.

it is likely to be extremely cold. I went there at Christmas once and I have never been so cold in my life. I remember wearing four layers under a big coat and I was still freezing. You'll need serious gloves, and a decent hat which covers your ears.

Apart from that, it's a wonderful city. My visit was twenty years ago so there wasn't yet much in the way of western shops and restaurants. I'm sure it's different now.

The tickets have to be time-stamped in a machine before use and if you try to use one when not stamped, you get fined. The transport police enjoy nabbing unwary tourists.

Its out of the city but the Sedlec ossuary (AKA the bone chapel) at Kutná Hora is worth visiting - about an hour on the train.

...including synagogues and cemetary is well worth a visit. Poignant, to say the least.
For a great view of the city, go up the funicular to Petrin Hill (tram to Ujeszt stop, just over the bridge one down from Charles bridge) where there is a small version of the Eiffel Tower you can go up.
Go for a walk round the castle too. You can get the tram up to the back entrance. The square at the front of it is v nice in winter, and you can play "Spot the site of the defenestration".
Avoid the Town Square. The astronomical clock is somewhat dispappointing, IMHO.
Strahov monastery is also worth a look if you have time, it's near the Castle.
It's a great city to wander in. Are there any walking tours?

The Jewish quarter too. If you can get out for the day Theresenstadt is well worth seeing.

Also I made a point of visiting Jan Palach's grave http://www.janpalach.com/ which I found moving.

Avoid the taxis at all cost. The drivers will rip you off.

The Museum of Communism is also worth a visit, strategically and amusingly placed above McDonalds.

The Czechs have a refreshing candour when it comes to talking about their past. Quite a few of the public monuments make pretty bold statements about communist oppression. There's none of this "we all made mistakes, but let's forgive and forget" stuff. They are pretty clear about what happened to their country.

Also ... Prague has more bookshops per square mile than any other place I've been.

Very much a must imho. The museum dedicated to the concentration camps is exceptionally good and extremely moving. I know you are going over xmas and probably want a joyous time but the exhibition of paintings done by the child inmates of Sachenhausen moved me to tears and I dont recall ever seeing anything so powerful.

I'd be on this like Rice/white interface but the only place I go is to visit my Grandmother. (I'm British/Czech) but I've asked about.
http://praguebykaty.wordpress.com/
http://aktualne.centrum.cz/domaci/fotogalerie/2011/09/22/zapomenuta-mist...
that one is in czech but Google translator should help,if not,pm me

http://www.zapomenutapraha.cz/
as is this,click on the zone you want,then on any photo you see you like.
this is the one i recommend to all the people i know who visit
http://www.myczechrepublic.com/index.html

as Clive said AVOID taxis unless you agree on the fare before you get in.
Have a great time.
Bez peněz do hospody nelez.