LTT and Tony's will probably be open again this year during the party itself.
The Castle, Crystal Palace, and the Plaza all take ADRs up until 6:00p only; they are not open during the party itself.
Any time between 4:00p and 6:00p is good so you don't miss any of the party.
Cosmic Rays, Casey's Corner, the bakery, Pecos Bills, Pinocchios Village Haus, and Terrace Noodle Station are some that I remember being open for counter service.