With links like '10 Things Not to be Missed in Granada' and '100 Suggestions to Enjoy Oneself in Granada', the official tourism website for the city should be able to provide you with plenty of information: http://www.turgranada.es/?id_idioma=2
Be careful of the shoe-shining gypsies, they practically throw themselves at your feet as you are walking and start polishing and then demant an excessive amount of money. We we warned and so wore plastic shoes, which confounded them.
Go to the tourist office who will help you find the current best places to visit for Flamenco dancing etc.Be VERY careful if you venture into the Sacramento district especially at night.Robberies do happen and most of the so called Gypsy flamenco caves and bars are an absolute ripoff But do explore the place apart from the Alhambra which is awesome.I lived less than two hours drive away for many years and visited often.The student area is a great place to eat and along the riverside only a brook really but it gets elevated! is anm amazing old Roman bath-house.It's a lovely walk down the hill from the Alhambra into the town ENJOY!!!!!!!!!!!!!!