Well I'd chose Budapest, Prague or Vienna for christmas and I like Bucharest

I would stay at the Hiltonbecause it is right across the street from Revolutionary Square.

Ask for a view to the Revolutionary Square.

I usually do not like to tell people whereto eat but you must go to Caru cu Bere Restaurant.

It is along the main street Victory Avenue( Victoria Calle).
(About 4-5 blocks past the Revolutionary Square)

It is worth it just to see the inside of the restaurant.

It is not an expensive place.

Go to www.inyourpocket.com and look at the online guide for Bucharest.

what you want to see / visit? On 1st and 2nd January I suppose that most of the places (mnuseums) will be closed.
For New Year Eve you have to make a reservation at a restaurant at least one month in advance.

Do you want to stay all three days in Bucharest, or you want to go to Sinaia or Poiana Brasov for 1-2 days?

Dunno what you're looking to spend...but if you're looking at hostels in Bucharest, try the Green Frog. I stayed there several days last year, on the conclusion of a Danube bike tour, and found it a comfortable, friendly place. The lady running the place is a sweetheart, and her brother, a former merchant seaman, is a character.

Beware the taxi drivers!! Crooks and shysters, worst in Europe that I've ever encountered. One of my favorite travel horror stories involves being kidnapped and dropped in an unfamiliar part of Bucharest at 2AM when we contested a 5x normal fare. Long walk home, it was. When we mentioned this to the lady running our hostel in the morning (couched in terms guaranteed not to cause alarm, like "Uh...the police didn't come looking for us this morning, did they?") she expressed regret and the opinion that that sort of thing was pretty normal behavior for those guys. IIRC (not sure) the normal taxi fare from the airport into the central city is about 20 euro. A pair of fellow guests at the GF were charged 200, and not knowing the proper amount, paid it.

Pretty good 'free walking tour' of the city is available - I went on one. Not free, of course, one is expected to tip the guide ten euro or so pp, well worth it. Good nightlife in the central city. Gorgeous women in Romania. Enjoy the trip!

Remember that over New Years it could be snowing, cold, slippery etc.

I would pick out 4-6 places you want to see in Bucharest and visit those places.

For example if you are going to be staying near the Revolution Square, you are walking distance to many of the major places, including of course..

The Parliament Palace

Let us known where you will be staying and places you might have on your list of places to see.