Most people spend New Year's Eve having a meal with their family then go out after 12pm to bars and pubs.
You can tell that people have been with their family because many people wear suits. (this must be to keep the mothers happy)
New Year's Eve is quiet in the street until after 12.
Many restaurants are closed and if you want to go to a restaurant it is a good idea to find out beforehand if it is going to be open.
Many bars and restaurants have a Cotillon which has a fixed price and you can drink as much as you like and they also provide food.
The only cotillon I have ever been to was not very good. In my opinion a cotillon is only a good idea if you know lots of people in the bar and you really want to spend the whole evening in one place. It would probably only be a good deal if you drink enough alcohol to need hospitalization.
At 12pm most people put the TV on and watch the clock in Madrid. In Spain a grape is eaten for each stroke of the clock at 12pm on December 31st. Each grape is supposed to represent one month of the new year)
In Granada several thousand people go to Plaza del Carmen which is the Ayuntamiento Square. (the town council) There are lots of fireworks, cava (Spanish champagne), corks flying, paper hats etc.
After 12pm many people will stay up most of the night partying and probably won't get up until 6pm the next day.
If you don't like heavy drinking and feeling obligated to be merry you may find it a good idea to go to bed at 10pm with a cup of cocoa and a good book.
On 6th January there is a Christmas parade, the principal characters are the "magic kings" who drive around the city on a float and shower the children and people with sweets and other presents. Some enterprising adults use inverted umbrellas to catch more sweets.
On 2nd January there is celebration of the taking of Granada by the Christians in the Plaza del Carmen.
(Día de la Toma) After over 700 years of moorish rule the Arabs finally surrendered on the 2nd January 1492. If you read the history of the shameful ethnic cleansing, breaking of solemn pacts and general unchristian and barbaric behavior which happened afterwards it is difficult to know why it is a thing that should be celebrated in a triumphal way.
If you are single (especially a single girl)you can go up to the Torre de la Vela in the Alhambra on the 2nd of January and ring the big bell. Apparently it will considerably increase your chances of getting married during the year. If you are staying in the Albayzin I recommend that you go out for the day because the sound of the bell ringing all day can be annoying.
This page may help you understand the Spanish vocabulary of Christmas.http://lingolex.com/christmas.htm