We have done Riga, Prague and Dublin for New Year and were after a similar experience. i.e cheap beer, lots to see and a great experience on ney years eve itself.
Dare I be controversial and suggest (based on the places you've already visited) that you'll find Budapest a little dull in comparison.
An alternative might be Tallinn (I can highly recommend the Three Sisters Hotel), or perhaps for a complete change of pace Amsterdam (nothing can prepare you for the pyrotechnic madness that is New Years eve!).
Dull?...I've beento Budapest a few times and found it anything but dull!...I will add that it does get VERY cold at Christmastime. Pricewise Budapest isn't much cheaper than at home, except in out of town areas. Theres lots to see there, I'd leave it till May when the weather is warmer, (if you're just going for the sights etc)
John I think you've misread the question. New Year seems to be the key factor. I.E have you been to Budapest during New Year, and if so how does it compare to the other destinations at the same time.