Cheap hotels in Center: Cathedral, Granada
Granada's cathedral marks the heart of the city. Off of this imposing structure branch cobblestoned streets, vibrant as the flamenco dresses hanging from doorways and buzzing with tourists and assorted shops (and overpriced cafés). The Capilla Real houses the crypt of Ferdinand and Isabella, and a five-minute walk to the west will put you in university territory—and at the stunning Monasterio de San Jerónimo.
It's area is a short, but uphill, walk to the Alhambra from some hotels in this neighborhood, while other hotels are are a bit further away. The main train station is within an easy distance. Beware, near the cathedral, of the harmless-seeming ladies who may approach and want to read your fortune.