1. La Alhambra, the Red Castle (al-qala´aal-hamra) Once you visit the Alhambra it becomes easy to understand why this is Spain´s most visited tourist attraction. Its beauty is in its stunning gardens, its many monuments, the museum, but also in the views from La Alhambra of Granada, the Sierra Nevada, and rolling hills of the Andalusian countryside. Last but not least, the views from Granada of the red castle are simply amazing and have inspired poets, painters, and lovers from all over the world.
2. The Albaycin. The old Muslim quarter that faces the Alhambra is an open-air museum with romantic palaces with secluded gardens, fantastic view-points like Mirador de San Nicolas, white houses, narrow streets, bars, and shops. We recommend you lose yourself in the Albaycin during one morning or late in the evening to enjoy amazing views at dusk. You can find our recommended itinerary in the Albaicin here.  Once at the Albaycin we do also recommend to continue your visit and explore El Sacromonte, the gipsy district with also fantastic views and that will also transport you to a different world. 
3. Gastronomy. Not only you will find it very affordable, but also authentic. The eclectic nature of Granada is also felt in its bars and restaurants. The mixture of flavors and aromas is part of Granada and dates some centuries back to our globalized days of fusion food.
4. Sierra Nevada and Alpujarras. The park of Sierra Nevada offers one of the best trekking in Spain. For ski lovers, the mountain range is one of Spain´s top ski resorts. Its top peak with the beautiful name of Mulhacen is at 3,478 meters, 11,410 feet and it ranks in second place amongst Spain´s highest peaks.The Alpujarras is part of the Sierra Nevada. A region of spectacular landscapes, dotted with white villages, it was historically occupied by the Berbers and then, when Granada was occupied, also by the Moors from Granada that fled to these lands. Besides the beauty of its landscapes, a wealth of culture and fascinating villages like Pampaneira await you, and we should not forget that one of Spain´s most famous Jamon (Spanish ham).
5. Street-art in Granada. Spain is not particularly well-known for the quality of street-art but Granada is clearly an exception. Most Graffiti art is to be found in the Realejo quarter, which is not far from the Alhambra. Raul Ruiz is an artist known as “El niño de las pinturas” (the kid who paints) who is behind many of the paintings and who may have inspired others to follow his art. Some of the places where you will be able to enjoy excellent examples of street art in Granada include: Santo Domingo School, Plaza de Joe Strummer, Calle Molinos 44, hotel Molinos, with a fantastic version of Rodin´s The Thinker.

You can find more ideas and things to do in Granada in this article.