Riding is the signature Tupiza experience. Several agencies on Avenida Pedro Arraya around the train station rent horses with a guide for two-hour, half-day, full-day and multi-day rides. Prices are low by South American standards and the horses are generally well looked after.
A typical half-day trip will take you out through the Quebrada de Palala, up to a viewpoint and back via a slot canyon. Multi-day trips push out toward the back country and the high pastures above town. Wear long trousers, take a hat and bring more water than you think you need.