Madrid and Berlin have huge parties for new year's eve and lots to visit and do, but I'm not sure whether it would be easy to find any accomodation anymore for this year.
I agree about Madrid and Berlin. Accomodation will always be at a premium price 30-31 Dec so cheap might not be possible as well. Vienna and Prague do a great New year, but once again prices go up. Munich might be a cheaper place for your beer and sausage.