Following is our suggested itinerary, please note that you may extend the number of nights in each city:

Day 1: Madrid
Madrid is a city of great contrast and tendencies that provide a feast for the eyes: the Old City, the innumerable churches and convents, the Madrid of the Hapsburgs, the Royal Palace, the Puerta de Alcala, the Retiro Park, etc. Every façade, corner, statue or park has its own particular charm. It`s museum mile offers more masterpieces per square foot than anywhere else in the world; the stellar Prado with its El Grecos and Velazquezes; the Caravaggios and Rembrandts at the Thyssen-Bornemisza; and the Dalís, Mirós and Picasso's wrenching Guernica, at the Reina Sofía.
(Madrid to Cordoba - 245 miles - 4 hours)

Day 2: Cordoba
The Caliph?s Dream
This ancient city, which has been declared World Heritage Site, is a living legacy of the diverse cultures that settled in it throughout history. Very few places in the world can boast of having been the capital of Hispania Ulterior under the Roman Empire, and the capital of the Umayyad Caliphate. Such splendor is palpable in the intellectual wealth of this centre of wisdom and knowledge that has seen the birth of figures like Seneca, Averroes and Maimonides. To take a stroll through the historic quarter of Cordoba is to discover a beautiful network of small streets, alleys, squares and whitewashed courtyards arranged around the Mosque-Cathedral, which reflects the importance of the city during medieval times and which is a real symbol of the capital. Also of interest is the Synagogue, the walls surrounding the old city, the Roman Bridge, the royal stables. Loosing oneself in the small, winding streets allows the traveler to truly experience the flavors of Al-Andalus.
(Cordoba to Cazorla - 115 miles - 2 hours and 20 minutes)

Day 3: Cazorla
Natural Treasure
The earliest traces of human presence in Cazorla can be found in the natural rock shelter of Valdecuevas and date back to the 6th millennium BC. During the times of the Iberians, Cazorla belonged to the important city of Toya. Romans, Visigoths and Arabs settled these lands, which gained importance after the 13th century.  In the enticing old quarter of Cazorla, highlights for visitors include Yedra Castle and the Museum of Arts and Traditions of the Upper Guadalquivir (Museo Artes y Costumbres del alto Guadalquivir).  The Castle of La Yedra stands at the foot of the Cazorla Nature Park, Segura and Las Villas. You can truly immerse yourself in nature at the Nature park with spots such as the Torre del Vinagre Interpretive Center, Iruela Castle and Collado del Almendral Game Park. This extremely beautiful natural area will surprise you during any season of the year with its lovely scenery. The Parador stands in the heart of nature, a haven for those seeking peace and quiet.
(Cazorla to Ubeda - 28 miles - 50 minutes)

Day 4:  Úbeda
A Renaissance Delight
The beauty of Ubeda's townscape is sure to impress you. Green olive groves mark the edge of this historic town, giving way to façades of carved stone amidst whitewashed houses. Founded by Abderraman II and the object of disputes between Almohads and Almoravids, this town, nestling among serene olive groves, is home to the very finest of the Spanish Renaissance. It was during the Arab period that Úbeda became a population center. In 852 the town was walled, and during the 11th and 12th centuries, it was conquered successively by Almoravids and Almohads. But Úbeda, declared a World Heritage Site by UNESCO, is noteworthy above all for being the Jaen town with the greatest wealth of monuments. A spectacular ensemble, in a perfect state of conservation, where you can admire beautiful Plateresque façades, altarpieces by the great artist Alonso Berruguete and patios with arched galleries on two levels. Of special note are the Holy Chapel of San Salvador and Santiago Hospital, the palace of the Cadenas family and the church of Santa María de los Reales Alcázares. Waking up in Tuscany, that is the unanimous sensation of those who stay in the Parador of Úbeda, a formidable 16th century palace.
(Ubeda to Jaen - 36 miles - 55 minutes)

Day 5: Jaén
The Almoravid Legacy
The capital of the province with the largest number of protected areas in Spain is in a landscape surrounded by olive trees. Its origin as a centre for Arab caravans, its importance as a strongpoint on the Castilian-Muslim frontier during the Reconquest and its current dedication to producing olive oil make it a must for visitors.  
The oldest part of Jaén is dominated by the Arab fortress that stands on Santa Catalina hill. From this height you can enjoy one of the best views of the city and the Guadalquivir valley. The Castle of Santa Catalina currently houses the Parador de Turismo.  At its feet, the oldest districts of the Andalusian city unfold, spread around the churches of La Magdalena, San Juan and San Ildefonso. But the core of this historic quarter is Santa Iglesia Cathedral. It is a monumental Renaissance building from the 16th century, which contrasts with the popular-style white houses surrounding it.  The legends that were born in its streets and corners, in the façades of its palaces, within its cathedral, are the greatest fascination of a guided night-time visit.
(Jaen to Seville - 180 miles - 3 hours)

Day 6 and 7: Seville
End in captivating Seville, best known for the impressive Cathedral with its Giralda tower, as well as the Alcazar, which also serves as a visiting residence for the Spanish Royal family.   Wander the Barrio Santa Cruz and the area around the Alcazar (with stops now and then in one of the many appealing tapas bars, cafes or restaurants for some refreshment). Grab a taxi and go to the Maria Luisa Park.  Jump into one of the many horse-drawn carriages and let them leisurely chauffeur you around the park and over to Plaza España.  Be sure and climb up into the tower for wonderful views out over the city.