La Alhambra is amazing, but the city is great as well. Orange trees grow everywhere, and don't forget to sip from the numerous fountains that are constantly running.
Insider Tip:Granada is known for its free but delicious tapas. Look around (esp. off touristy areas) and an average meal could cost you 2 euros for a drink and tapas. I recommend La Belle y La Bestia as a starting point.