One of the most wonderful parks is Jardim Botânico de Brasília, located in Setor de Mansões Don Bosco in Lago Sul. It only has one entry, and the cost is $5 reais per person. It is closed on Monday.
The park showcases the Cerrado, the vegetation of the surroundings of Brasilia. It has network of mountain bike and running/walking tracks. You can get lost in that park.
In the center of the park you find the visitor center, a really cozy restaurant (service is slow, but..), a picnic area and the Japanese Garden. On Sundays, several artisan producers sell their goods there, like breads, honey, herbs, cachaça and wooden toys.