The main attraction in the city centre is the Cristo de la Concordia statue, which makes a pleasant excursion. There are a number of colonial churches around the city centre, or if you want to get a feel for present day Cochabamba, head to one of the throbbing street markets.
The Museo ArqueolÃ³gico has a good display of Bolivian archaeological pieces, or you could go and visit the pre-Columbian ruins at Incaracay or Incallajta. For an alternative city tour, hire a bicycle (at The Spitting Llama bookstore or Ranabol tour agency) and follow the cycle of path from the north of the city, past the Cristo de la Concordia to the Laguna Alalay to the southeast of town.
The closest place to get in touch with nature is Parque Nacional Tunari, just a few kilometers from the city. The national parks of Carrasco and Torotoro, and the tropical region of the Chapare, are all within easy reach of the city.