New Year holidays in Hungary
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.
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):
The following restaurants are closed: Malomto-Dec 31..Jan 1 (NY06/07).