Right across the Río Rímac from Lima  is the downtrodden Rímac neighborhood, which began as a mestizo and mulatto barrio during the viceroyalty and was refurbished in the 18th century by the Lima aristocracy. All the sights here are close to the Plaza de Armas—take a taxi, as assaults are common in this area.
The Museo de los Descalzos (end of Alameda Los Descalzos, tel. 01/482-3360, 10 a.m.–1 p.m. and 3–6 p.m. Tue.–Sat., 11:30 a.m.–6 p.m. Sun.) was a convent and spiritual retreat for the Franciscans. Today it contains interesting and elegant cloisters, a chapel with a gold-covered baroque altar, an elegant refectory, and a gallery with more than 300 paintings from the 17th and 18th century—including a masterpiece by Esteban de Murillo.
On the taxi ride home, ask your taxi driver to pass the nearby Paseo de Aguas, an 18th-century French-style promenade where Lima’s elites strolled along its artificial waterways. All that remains today is a neoclassic arch, hidden next to a towering Cristal Beer factory.
Nearby is the giant Plaza de Acho, Lima’s bullring, where bullfights are held early October–early December. Inside is the Museo Taurino (Hualgayoc 332, tel. 01/481-1467, 9 a.m.–6 p.m. Mon.–Sat., US$1.50), which contains a wide range of bullfighting relics.
Towering above Rímac is Cerro San Cristóbal, where Francisco Pizarro placed a cross in thanks that Quizo Yupanqui and his Inca army did not succeed in crossing the Río Rímac into Lima  during the Inca rebellion of 1536. Today the hill is encrusted with a dusty pueblo jóven named Barrios Altos. There is a lookout over Lima at the top, along with a small museum and a giant cross that is illuminated at night. To reach the top, take a taxi from the Plaza de Armas (US$6) or wait for buses with English-speaking guides that leave from the Municipality (US$3.50).