Take a stroll in Parque Bolivar, the city´s favourite lovers´ hangout. Just don't step on the grass. At the upper end of Parque Bolivar stands Bolivia's supreme court, and at the lower end is estacion Aniceto Arce, Sucre's former train station which is currently not in use. If you don't get your fill of old trains in Uyuni, there is another one within the station precinct. Ask permission from the token security guard before you enter, as there is a guard dog here (although she is usually playing with her puppy). Also in Parque Bolívar is a charming miniature reproduction of the Eiffel Tower. If you decide to climb to the top, be warned that any schoolkids who happen to be around will gleefully climb up with you, and proceed to rock the entire structure as alarmingly as they can.
