The Baryon acoustic oscillations from Integrated Neutral Gas Observations (BINGO) telescope is a new 40-m class radio telescope to measure the large-angular-scale intensity of Hi emission at 980-1260 MHz to constrain dark energy parameters. As it needs to measure faint cosmological signals at the milliKelvin level, it requires a site that has very low radio frequency interference (RFI) at frequencies around 1 GHz. We report on measurement campaigns across Uruguay and Brazil to find a suitable site, which looked at the strength of the mobile phone signals and other radio transmissions, the location of wind turbines, and also included mapping airplane flight paths. The site chosen for the BINGO telescope is a valley at Serra do Urubu, a remote part of Paraiba in North-East Brazil, which has sheltering terrain. During our measurements with a portable receiver we did not detect any RFI in or near the BINGO band, given the sensitivity of the equipment. A radio quiet zone around the selected site has been requested to the Brazilian authorities ahead of the telescope construction.