My favorite hotel in Nice by far is the Hotel La Suisse. Relatively reasonable prices and unquestionably the best view of the city you can get. Make sure to specify you want a room with a view (the rate will vary)

http://www.tripadvisor.com/Hotel_Rev..._Provence.html

Strong points are the view, the service (smaller hotel so more personable staff), and the location. It is one of the closest hotels to the "vieux nice" which is where you find the flower market, many great traditional nicois restaurants, touristic shopping. I believe they also have an accord with the Castel Plage in front, though that's probably not a selling point for a jan/feb stay.