In the city will be plenty of NYE dinners at restaurants and parties on music locations, in all kind of music genre. But both are in common ridiculously overpriced, comparing non-nye days.

You can count for a dinner from 100 till 4-500 Euro pP, party entry like from 30 -50 Euro.

But I guess, everywhere in the world, all services are overpriced between 23.12 and 2.1

Fireworks as mentioned, no state official (this is on 20th August) - just from locals, though every year there are designated place on Vörösmarty square / Heroes square, where bigger crowd comes together at midnight (mostly younger peeps), and shoot the fireworks and drink champagne with randoms.