A city of over 200,000 people, with a varied history of inhabitation that ranges from its original Roman rule to the Moorish conquests of the 8th century and the Christian victors that followed, Granada's greatest asset is its culture. There are plenty of monument-adorned plazas and culturally distinct neighborhoods, while the mega-complex of Moorish architecture known as the Alhambra is the indubitable tourist centerpiece of the region.
The Alhambra is a preserved palace and fortress ruin atop a hill in the center of the city and is the heart of Granada's tourism industry. The ancient towers of the Alcazaba provide the best panoramas of the city, while the Palace of Charles V, the newest part of the complex, houses the two museums of the grounds. The Museo de la Alhambra has a fine collection of related artifacts while the Museo de Bellas Artes has quality art exhibits. The central focus of the Alhambra is the Palacios Nazaries, a former Moorish royal palace of ornate archways and splendid woodwork; this is also where you'll find the heaviest concentration of tourists. To get away, walk the extensive gardens and fountains of Generalife, where royalty would frollick the summer hours away. Just be aware that entrance to these attractions is quite sought after depending on the season and some areas are only open at certain times of the day. Be sure to check ahead so that you may enjoy everything that you'd like.
Exploring the grounds of the Alhambra is only one part of seeing the massive attraction; viewing it from outside the walls is also an integral part of the experience. The Muslim neighborhood of Albaycín is an attraction in its own right, but most enter this hillside community for its superlative views of the Alhambra, whether from the Mirador de San Nicolas lookout or from any of the numerous overpriced restaurants and cafes uphill from the Plaza Nueva. There are many lovely little nooks and crannies in this neighborhood, which is a whirl of small plazas (the Paseo de los Tristes and the Plaza Larga are excellent) and narrow, cobblestoned streets (Carrera del Darro and Calle Calderería Nueva are great for a stroll). East of the Albaycin and alternately more unique and less touristy is the neighborhood of Sacromonte. Home to a large Gypsy population, many of the dwellings are built into hillside caves; this area is popular both for its flamenco shows and for its views of the Alhambra.
South of the Alhambra is the modern center of the city, which hums around the Puerta Real. This is the crux of Granada's modern amenities, with a number of attractive buildings of a classical nature and consumer culture converging to present the city at its contemporary best. Further south is the former house of Federico García Lorca, which is now a museum in his name surrounded by a beautiful public park. There are also two attractive churches in the area worth a look; the Basilica Nuestra Señora de Las Angustias and the Iglesia de Santo Domingo. North of the Alhambra are a handful of newer neighhorhoods notable for their broad streets and classically designed buildings; there are a few religious buildings and plazas worth walking through, although this is not where you'll find most travelers unless you are looking for a cheaper bite to eat. While you're here, take a look at the Hospital Real, a 16th century building that overlooks the fountains of the Triunfo Gardens, and is now part of the university. You may also enjoy the baroque stylings of religious institutions like the Cartuja Monastery, the San Jeronimo Monastery, and the grandiose Basilica San Juan de Dios.
Granada is also within a few hours of cultural powerhouses like Seville (known for its exceptionally large Gothic cathedral) and Cordoba (known for its incredible old town and the Mezquita mosque/cathedral at its center, as well as the ruins of the Roman capital, Medina Azahara). Combine these cultural elements with the many styles of adventure found within a day trip of Granada and you've got the beginnings of a fantastic trip.