Hi in Spain our holiday season extends into January, with the main celebration being Dia de los Reyes Magos (three kings day) on January 6th. Know that on the night of Jan 5th most cities in Spain have a big parade of the Three Kings (Cabalgata De Los Reyes Magos), it will be a great festive experience in our local culture. There are really big Three Kings parades in Barcelona and Madrid.
FYI many restaurants will be open on Christmas Day (Dec 25), but it is a very popular time to eat out for the traditional Christmas lunch, around 3 pm, for local Spanish families so you may need to reserve in advance. However most stores will be closed Christmas Day (Dec 25).
Also, be sure not to miss our Christmas markets in Spain! Our Christmas market tradition is a little know part of our culture (It's not just the Germans lol). Since we mainly celebrate the Three Kings Day (Jan 6), you will find most of our Christmas Markets are still up into early Jan. For example, in Madrid the Plaza Mayor Christmas Market is great.
Here is a English language article about some of our amazing Christmas Markets in Spain:
https://theculturetrip.com/europe/spain/articles/12-magical-christmas-markets-to-visit-in-spain/
Regarding NYE, Think of Madrid as the New York city of Spain when it comes to New Year's Eve, and think of Madrid's Puerta del Sol as the Times Square. The most famous New Year’s tradition in Spain is eating 12 grapes, one for each gong at midnight. I think you'll have a blast if you head over to Puerta del Sol in Madrid during NYE, with a bottle of Cava (sparkling wine) in one hand and a handful of grapes in the other!
P.S. During the holiday season, we have a tradition in Spain of eating Turrón – a nougat-like sweet. I would be on the look out to try some. For sure, you can find a great selection of different turrónes at El Corte Inglés.