Popayán, also known as "La Ciudad Blanca", is a city and the capital of the Cauca department in Colombia.
Take bus #7 or #9 (06/2019: 1,800 COP) going towards Río Blanco neighborhood and ask the bus driver to leave you at the Terpel gas station (02°30′28.91″N 76°32′50.66″W) at the Northern limits of Popayán. This is where you can start hitchhiking and asking people for a ride.
East towards Tierradentro, La Plata (Colombia)
Take bus #7 or #9 (06/2019: 1,800 COP) going towards Río Blanco neighborhood and ask the bus driver to leave you at "Cruze Totoró" (02°30′38.12″N 76°32′40.38″W). Here put a smile on your face, position yourself visibly and stick your thumb out.
Take any bus going towards Timbío (06/2019: 2,600 COP), either from the main bus terminal of Popayán or "Terminal Trans-Timbío" on Carrera 17 (02°26′33.84″N 76°36′54.91″W), and ask the bus driver to leave you at the "Estación de Servicio y Hotel Mi Bohio" (02°25′11.45″N 76°37′58.96″W). This is where you can start hitchhiking and asking people for a ride. The bus company charges you the same as if you would be going all the way to Timbío, but as there are no local buses going this way, it's your only real option to get out of the city on your way South. Please be aware that this spot is also way more promising than going all the way to the village of Timbío. The next spot and gas station worth stopping at is located just before the town of Rosas (02°15′56.06″N 76°44′21.24″W).