Start with the cathedral, in the Plaza Virgen de los Reyes. Then climb the Giralda, the minaret of the former Moorish mosque. Walk down Avenida de la Constitución until you reach the Archivo de las Indias. Behind the archives is the Alcázar, surrounded by high walls. Allow at least a couple of hours to explore this superb Moorish fortress and palace, surrounded by lush tropical gardens.
Backtrack to the Giralda and the Plaza Virgen de los Reyes and plunge into the Barrio de Santa Cruz, a tangle of narrow streets and squares lined with orange trees that was the home of Seville's Jews in the Middle Ages. While you're in the neighborhood, don't miss the baroque Hospital de los Venerables, a hospice for the elderly with a plant-filled patio and several notable paintings. On Calle Santa Teresa is the Museo Casa de Murillo; from there you can stroll through the Jardines de Murillo. At the far end of the gardens is the University of Seville, once the tobacco factory where the mythical Carmen worked as a cigar roller. Across the Glorieta de San Diego is the Parque de María Luisa, which encompasses the Plaza de España at its east end as well as the Plaza de América at its south end. In the Plaza de América you can find the Museo Arqueológico, with marble statues and mosaics from the Roman era. Opposite is the Museo de Artes y Costumbres Populares. Head back north along the Paseo de las Delicias toward the city center. Near downtown Seville, on Avenida de Roma, is the baroque Palacio de San Telmo, home of the Andalusian regional government. Behind the Palacio is the Mudejar-style Hotel Alfonso XIII. On the north side of Puerta de Jerez is Palacio de Yanduri, birthplace of the Nobel Prize winner Vicente Aleixandre.
Walking toward the Guadalquivir River along Calle Almirante Lobo, you come to the riverside Torre de Oro, which stands opposite the Teatro de la Maestranza. Behind the theater is the Hospital de la Caridad, with a collection of works by Seville's leading painters. Continuing north along the river, you reach the Plaza de Toros Real Maestranza. Finally, head away from the river toward the Plaza Nueva, in the heart of Seville, and have a look at the ayuntamiento.
If you have energy and two more hours, walk north from the town hall along the pedestrian Calle Sierpes, Seville's most famous shopping street. Backtrack down Calle Cuna, parallel to Sierpes, stopping at No. 8 to see the Palacio de la Condesa de Lebrija. Continue down Calle Cuna to Plaza del Salvador and the Iglesia del Salvador, a former mosque. Walk up Alcaicería to Plaza de la Alfalfa and along Sales Ferre toward Plaza Cristo del Burgos -- in a small alley off the square is the Casa Natal de Velázquez, where the painter was born in 1599. From Plaza Cristo de Burgos follow the narrow streets Descalzos and Caballerizas to the Casa de Pilatos, believed to be modeled on Pilate's house in Jerusalem.
A number of other sights are scattered throughout northern Seville and require separate trips. If you're an art lover, set aside half a day for the Museo de Bellas Artes. From here, head down to the river and across the Pasarela de la Cartuja bridge to the island of La Cartuja. Take a look at the Carthusian monastery, now home to the Andalucian Center of Contemporary Art. Another half day should be set aside to explore the Triana neighborhood, on the river's western bank. To visit the Basílica de la Macarena, site of the Virgen de la Macarena, it's best to take a taxi from the city center. Other religious sites in the Macarena area are the Gothic Convento de Santa Paula and the church of San Lorenzo y Jesús del Gran Poder, where colorful floats used in Seville's Holy Week processions are on display. If you just feel like a leisurely trip, hire a horse-drawn carriage; alternatively, you can hop on a city tour bus.