Gellért Baths. NY06/07: on Dec 31, open until 1pm only.
Széchényi Baths. NY06/07: on Dec 31, open until 1pm only. On Jan 1, open from 8am.
Rule of thumb for dinner on Dec 31 is: either a restaurant is open all night (and is closed for NY program well before it starts), or it doesn't work at all. Therefore, you're very unlikely to find a dinner even for 7pm or 8pm without buying an overnight program.
For Christmas and New Year days, there're food stalls set up at Vörösmarty tér offering skewer meat, pancakes, sausages and sauerkraut, vegetable mix and hot wine.
Most restaurants/clubs at Liszt Ferenc tér have some programs for New Year night (NY06/07).
Besides, the following restaurants have an overnight program (NY06/07):
Cafe Negro: As of NY06/07, all seats were booked before evening of Dec 30.
The following restaurants are closed: Malomto-Dec 31..Jan 1 (NY06/07).
Buda Castle Labyrinth Minimalheadz New Years Apocalypse . NY06/07: Entrance 2500ft in advance, 3500ft upon arrival. Several dance halls right inside the labyrinths, each hall with its own DJs. Starts at 21.
Gárdonyi Géza Theater. Jan 1, 7pm (NY06/07): New Year Concert--popular classics; digestible modern dance; some laser show. The conductor jokes and plays with the audience (even makes it sing with the soloist), but all in Hungarian--so better have a friend to help you. Master of ceremonies resembles provincial soviet-time song contest. Performance is introduced by mayor of the town.
The concert attracts the creme of the town--therefore evening dress is strongly recommended. At the entrance, welcome champagne is served.