how long are you going for? if you have time, a trip out of prague to Cesky Krumlov is well worth it! ditto Kutna hora. I lived in Ceske budejovice a few years ago and spent a lot of time travelling around the country!
good veggie food is difficult in the CR, but I loved smazeny syr - deep fried cheese. desperately unhealthy, but great with tatarske sauce mulled wine, roasted almonds, fruit dumplings - all yum! christmas bread there is called vanocka and is gorgeous (must remember to get /fil to bring some over!). christmas sweeties also yum!
wenceslas sq is a tourist trap btw - i loved it as it felt so busy after ceske bud, but it's very westernised compared to other parts of the city.
metro is great for getting around - cheap and easily navigable.
watch out for pickpockets around karluv most (charles bridge); it's full of them, sadly.
behind the castle, within the castle complex though, there's the golden street (I think?), lots of cute wee houses - great fun!
communist museum (just off thr bottom of wenceslas sq above a macdonald and casino iirc!) is excellent, best museum i saw in the whole CR!
december is not necessarily freezing cold, but is often wet, always raining when we're visiting at christmas!
sorry for poor typing, my (1/2 czech) DS is sleeping on me at the mo