Don't just go to see the Alhambra! There is much more to see in Granada.

Albayzin
Check out the Albayzin (Albaicin), the original part of the city, dating back to the 11th century, with its typical whitewashed houses and winding, maze-like streets. The neighborhood abounds with nice bars, tea shops, and cafes as well as good restaurants. There's even a cooking school.

Calle Elvira
This area is located near Plaza Nueva, near the edge of the Albayzin, and is full of tapas bars, typical restaurants, and cafes.

Sierra Nevada
Did you even know there is an excellent ski resort just outside Granada? It´s a quick drive (or bus ride) away (about 40 minutes), and there is a variety of accommodations at the resort if you decide to stay a few days there.