I don't think there's a special place for that..

US: Where there are Justices of the Peace, they usually work inside of courthouses or other government buildings (e.g., a city hall).

In Australia a Justice of the Peace (JP) act as an independent and objective witness to documents people use for official or legal purposes. Usually JPs are volunteer (non-legal professionals) who have a table in a court house, shopping center or town hall, where they can sign copies of documents. A Juzgado de Paz - sounds like a Magistrate, who is the "judge" in the lowest level of court in most Australian States. The Magistrate's court can hear (judge cases) with damages of $50,000 or less.