Villarrica has no tour operator worth the name. What it has is a local guide whom SENATUR names on two of its official circuits, and between them they cover the two things the town is for.
The Circuito de Fe walks the seven churches of Villarrica and finishes 30 km out at Itapé, where the Santuario de la Virgen del Paso stands on the bank of the Tebicuary-mí and draws pilgrims every December. You can do it yourself — SENATUR says so — but the buildings are locked as often as not and a guide is the difference between seeing seven façades and seeing seven interiors.
The Circuito del Ao Po'i is the better one. Ao po'i is the fine openwork cotton embroidery that Paraguay puts on its shirts, and Yataity, 25 km north of Villarrica, is where it is made. The circuit takes you from an organic cotton finca through a working artisan's workshop to the museum and the Escuela de Salvaguarda, where you can put your hands on the loom. It needs booking ahead.
There is no website and no published price for either. One mobile, +595 982 502806, answers for both.
They publish no street address, so the pin here is the town.