Horseback riding can be done at the recommended Fundo Chincheros (8 km north of Puno on Puno–Juliaca Highway, tel. 051/35-5694, www.fundochincheros.unlugar.com [1], $25 pp half-day tour), a country hacienda in the valley just north of Puno [2] operated by the owners of the café Cecovasa in La Casa del Corregidor.
Apart from trail rides, the day is spent hiking through cactus forest, seeing vicuñas, and having a garden picnic next to a rare 17th-century capilla abierta, or open chapel. The controversial constructions, which were banned after 1680, allowed Spanish priests to baptize Indians without having to let them in the church.
Links:
[1] http://www.fundochincheros.unlugar.com
[2] http://www.moon.com/destinations/peru/lake-titicaca-and-canyon-country/puno