If you want to spend New Years Eve in Europe, book now, if you can find anything. That is a very popular time in Europe.
A few years ago, we decided in JUNE to spend Christmas and New Years in Germany, and I found that most places were already booked at that time. As one pension owner in the Black Forest explained it to me, many older people in Germany are alone at the holidays, so they come to the resort areas to be alone with others. We spent New Years (Sylvester) in a small pension in the Allgäu region of Germany. The pension itself had been booked a year in advance, but the owner is a friend, and he arranged for me to stay at his sister's house.