City center, site of commemoration of Bolivia's independence, where you can feed the pigeons and look at the Metropolitan Catedral of Saint Sebastian.
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Awesome archeological museum with mummies, deformed skulls, amazing pottery and other artifacts. Well worth a visit.
1760 convent that is restored for viewing.
Cochabamba's other popular square, next to city hall, and a little greener than Plaza de Armas, 14 de Septiembre.
The main hospital in Cochabamba, Hospital Viedma, has a cute little medical museum attached, with some amazing old x-ray machines. The museum is near the corner of Venezuela and Oquendo.
Dancing fountain light show at night. Occurs from around 20:00-22:00 and small entrance fee.