Fiesta Nacional del Mate in San Jose de Mayo
Documented on the ground as the Fiesta del Mate y Dia del Gaucho, this March gathering at the Sociedad Criolla Capitan Manuel Artigas grounds in San Jose de Mayo combines jineteada horsemanship, live music, craft fairs and mate culture, and is described by Wikipedia as the most attended festival in Uruguay.
San Jose de Mayo, the departmental capital of San Jose in central-southern Uruguay, hosts what Spanish-language Wikipedia describes in direct terms as the festival with the largest public turnout anywhere in the country, held each March on the grounds of the Sociedad Criolla Capitan Manuel Artigas.