Restaurants for New Year Eve dinner

Staying in Kyoto for Dec. 27-Jan. 2, 2020. What good restaurants can you recommend for a family New Year dinner? Maybe a Kaiseki restaurant? Are most restaurants open this time of year?

"Are most restaurants open this time of year?"
no,. I think most are closed or closed early.

it is better that you start thinking from the point which restaurants are open near your hotel.

On New Year's eve, people stay at home with food they got beforehand including Osechi, which is traditional New Year's supper.
The only restaurants may be chain family restaurants, but these days even chain stores tend to be closed during New Year's vacation. Everyone wants to spend traditionally the most important days throughout the year with their family at home.

Restaurants are open during December even though they won't be serving New Year treats yet. Ask your hotel for recommendations.

For Jan 1 and 2, stick to your hotel for breakfast and dinner unless they have alternative recommendations. I'm sure the quality hotels have something New-Years-y to a certain extent. Then, for traditional fast food lunches, visit the food stalls in many of the shrines. Shrines are the places you'd want to visit during the first 3 days of the New Year, because that's where all the locals go for worship. You can even enjoy some food stall hopping.

That said, I did find a list of restaurants in Kyoto that are open on New Years, 2020.
https://www.leafkyoto.net/special/oshogatsu/

Among them, the only one themed on Japanese cuisine are the two below. The concept of the latter is that it's a sake (nihonshu) bar. I suggest you make reservations ASAP if you want to dine at either of the two.
https://aisani.net/
https://syuten-nishikawa.jp/

Hello - We are a family of 4 traveling from the US and will be in Kyoto from Dec 30 to 3rd morning. I've been looking for restaurants that will be open on 31st and 1st night as well and came across your thread. We found some restaurants in high end hotels like Four Seasons and Hyatt that will be open, though they are expensive. We were thinking we might do one night of take-out department store food and another night in Hyatt. Did you decide on something that you like?