New Years Eve
What does that mean?
Someone with a cane/walker who can't walk long distances or someone in a wheelchair where you need enough aisle space to get around.
Also, what do you want in terms of food and atmosphere? How much do you want to spend? What time are you planning to eat? Do you want a SF restaurant or elsewhere in the Bay?
Michale Mina is handcapped accessible but the tab is high. It has a little lift to the main floor. Normally not a place I'd recommend, but on New Year's I'll bet it is festive.
La Terasse is less pricy and is surrounded by a parking lot so it is probably one of the most accessible places either in terms of a short walk or wheelchair. However, if you are talking wheelchair I'd call them to make arranngements for a talbe that could easily accomodate that.
Depends on what you are looking for. I could make more recs but there's a lot of variables here.
Here's the opentable list sorted by neighborhood. If you see some that you like, then post about them and I can give you an idea of how accesible they are for your conditions.