In short
The Alhambra dominates the city from its hill, and the rest of Granada arranges itself around it: the Albaicín opposite, the Sacromonte higher up, the lower town below.
The Sierra Nevada is forty minutes away by road. You can ski in the morning and be on the tropical coast at Motril in the afternoon, which no other city in Europe allows.
What it really costs
Granada is markedly cheaper than Seville or Málaga, partly because the student population holds rents down. The centre stays affordable.
The free tapa with your drink is still the rule here, unlike the rest of Andalusia. Three drinks make a dinner, and that is not a figure of speech.
What nobody tells you
Entry to the Alhambra's Nasrid Palaces is at the exact time printed on the ticket, not before, not after, and being late forfeits it. Tickets go weeks in advance.
Summer regularly passes forty degrees and the city empties in August. April, May, October and November are the real seasons.
The viewpoints at Sacromonte and San Nicolás are free and give the view everyone is after, the Alhambra against the snowy Sierra. They are taken at sunset, and they are packed.