Awesome archeological museum with mummies, deformed skulls, amazing pottery and other artifacts. Well worth a visit.
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City center, site of commemoration of Bolivia's independence, where you can feed the pigeons and look at the Metropolitan Catedral of Saint Sebastian.
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.
A great arts and performance center based in an old slaughterhouse. They have rotating art exhibits, music performances, and other interesting stuff.