Southern Spain:
Day one. (Wednesday) Fly to Madrid. Stay at La Residencia de El Viso. The DK "Great Places to Stay in Europe" says "…delightful, good-value 1930s villa with a quiet garden. Once inside you can hardly believe that the location is so central…."
Day two. (Thursday) Day in Madrid to recover from jet lag.
Day three. (Friday) Morning in Madrid. Afternoon train to Toledo (1 hour). In Toledo see Cathedral and church of Santo Tomé. Stay in the Hostal del Cardinal (Hotel El Cardinal, Paseo de Recaredo 24, outside the city wall, near Puerta Nueva de Bisagra).
Day four. (Saturday) Full day in Toledo. Probably visit the Taller del Moro (has some 14th century rooms with Mudéjar decoration), the Museo de Arte Contemporaneo, and Museo de Arte Visigótico, the Hospital de Tavera, the Synagoga del Tránsito, and other attractions.
Day five. (Sunday) A day to get from Toledo to Cordoba. Either take a bus down highway E5 or take a train down to Cordoba. Stay at González, Manriquez 3 "In one of the Jewish quarter’s narrow streets, this hotel has a cool marble interior and Moorish arches leading to a pretty flower patio." — DK "Great Places to Stay in Europe".
Day six. (Monday) Full day in Cordoba with a second night at González. See Museo Arqueológico, the Mezquita, and the Medina Azahara.
Day seven. (Tuesday). It’s a short train (or bus) ride from Cordoba to Sevilla. In Seville stay at San Gil ("Classified as one of the hundred most interesting buildings in the city, the San Gil marks the careful restoration of an early 1900s mansion. A wealth of original detail remains, including a striking tiled entrance and enclosed garden with fountains, palms, an ancient cypress and original mosaics.
Day eight. (Wednesday) A full day in Seville. Visit the Alcázar, the cathedral, the Plaza de España, and walk around the town.
Day nine. (Thursday) A second full day to enjoy Seville.
Day ten. (Friday) Take a fast train back to Madrid in the morning. Friday afternoon and evening in Madrid, with a third night in La Residencia de El Viso.
Day eleven (Saturday) Day in Madrid. Go to the Prado at 2:30 (it’s free after 2:30 on Saturday). Fourth and final night at La Residencia de El Viso. Possibly fly back on Saturday night if one prefers an earlier return.
Day twelve (Sunday) The Prado is free in the morning. Afternoon flight back to the States.