Its very name evokes an era of scimitars, steeds and Saharan royalty. When North African Muslims ruled southern Spain in the mid-1300s the Alhambra was a city unto itself. Part palace, part fortress, the enormous edifice at the heart of bustling Granada incorporates 23 towers, two kilometres of original walls and sprawling manicured gardens. It's the largest surviving Muslim palace in the world - and the detailed stucco, marble, inlaid wood and exquisite mosaics are as well preserved today as when it was built about 1350, with water features weaving their way underfoot. Allow two days: one to roam the grounds and another to visit the ticketed highlights such as Palacio Nazaries, Jardines del Partal and the fortified Alcazaba. Buy tickets online (www.alhambratickets.com ) to avoid lengthy queues.
Lashed to the rocky outcrop at the point where the Mediterranean clashes with the Atlantic is the frequently overlooked port city of Cadiz. Founded by Phoenicians in 1100BC, it's a labyrinth of adorable streets and open squares. Many of the houses are now being restored as smart boutiques, tapas bars and ice-cream shops. Grab a cone of zesty lemon and follow your nose to Plaza de Topete (know locally as the square with the flowers markets). In spring a Rio-style carnival heralds 10 days of revelry, with singing, drinking and an almost mandatory uniform of fancy dress.
Even if Granada hadn't been blessed with the Alhambra it would still rate as one of Andalucia's must-see cities. Watch guitar-makers in front of crumbling shopfronts along Cuesta de Gomerez craft womanly curves from delicate timber. It's no tourist gimmick either - the guitar was invented in Andalucia. One of the most reputable craftsmen is Manuel Bellido, who can be found on Calle Molinos. Other regional specialities are leather, blankets and home furnishings decorated with lacquer inlaid with mother of pearl and silver.
As the name suggests, the town of Antequera is indeed antique, having been inhabited for more than 5,000 years. In the bustling streetscape are Roman baths, Gothic churches, a Moorish castle and millennia-old stone burial mounds. The largest is called Cueva de la Menga, where hundreds of skeletons were found. But it's just out of the city that the landscape takes on a truly surreal flavour. El Torcal National Park in the nearby foothills has been sculpted by winds for thousands of years. The result is a spooky landscape of limestone turrets, ridges and wormholes. Further afield, the equally unusual pink lagoon is a favourite stopover for migrating flamingos.
With three huge, walled enclosures, the Alcazaba is a magnificent Arab fortress at the top of a majestic mountain. It offers sweeping views over the pretty town of Almeria, including the old quarter, known for its cave houses, and the city's fortified cathedral, built in a Gothic-Renaissance style. Almeria has become the garden centre of Spain. Look for delicacies in the backstreets, including hearty gurullos (stews made with pasta), trigo (wheat, pork, beans and herbs), gachas (hot and spicy clam stew) and escabeche de sardines (fresh sardines in hot sauce).
6 Arcos de la Frontera
An appealing town that tests fears of heights and enclosed spaces, Arcos de la Frontera's whitewashed houses perch atop a narrow crust of earth pushed up into a ridge. Some streets are so narrow you can almost touch the buildings on either side. At the top of the square is an ornate church with mesmerising but gruesome sculptures of martyrs and a two-metre tall candle from the 1700s. At sunset, head to the square and watch ravens riding thermals below while bells peal across the farmland and goats bleat in reply.
7 Sleep in a mountain
Andalucia can be almost unbearably hot (40 degrees Celsius is common), and the occupants of towns such as Guadix found that the best solution was to dig in. The 3,000 cave houses carved into the mountainside stay at 18 degrees year round. Some are basic, but others have embraced more ornamental styles, with elaborate tiling, windows and brickwork. Stopping at Guadix is the perfect way to spend siesta time, sipping a cold beer and sampling tapas.
8 Jerez de la Frontera
A couple of centuries ago sherry was invented at Jerez de la Frontera - but not the sickly sweet stuff most people are familiar with. Spanish sherry is dry and has a faintly mineral quality. Sweet sherry, known as cream sherry, was invented in Jerez in the 1850s for unsophisticated British palates. It was a huge hit and soon English winemakers were heading to Jerez to become the first generation of British-Spanish sherry barons. High society in both countries intermarried and the result is a town with deep blue blood. Many old-school bodegas still don't allow cellar-door sales without an appointment, although all that's changing. For a spontaneous tipple just turn up at Gonzalez Byass cellars (www.gonzalezbyass.es ).
9 Flamenco festival
Invented in Andalucia in the late 1800s, flamenco has similar roots to the blues, deriving from poor gypsies known as Gitanos who used song to express their misery. Later, their passionate voices were joined by guitar, handclaps and haughty dancing in eye-catching costumes. Many small towns and bars, especially around Jerez de la Frontera, have impromptu flamenco nights, but some of the biggest festivals are in summer. Seville's Bienal de Flamenco, held every second September, draws the world's best performers.
10 Cradle of cubism
Malaga may be close to the tacky Costa del Sol, but it has managed to avoid at least some of the pitfalls of tourism. Its lively city centre offers several impressive monuments, including the remains of a Roman theatre. Malaga was the birthplace of Pablo Picasso and an excellent new museum (www.museopicasso  malaga.org), with almost 200 of his works, has just opened to celebrate his life and times.