South towards, well, not much... Ecuador
Take bus #49 from the centre. It heads out on the main road south, and you can get off at a couple of speedbumps at the edge of the city. You will see the bus take a different direction after 15 minutes or so. user:lukeyboy95 got offered his longest ever ride here, to Ushuaia in Patagonia... a whopper... anything can happen. Waited 1 hour for that ride. Do note, you start to get into hazy territory when crossing the Andes in the region south. Some routes are dangerous. You are best to cross La Plata, towards Popayan. Even though on google maps, it is a satisfying thick line, the highway is dismal. The plus is that you avoid Cali. Very little traffic crosses here.
Places to avoid
The city is very friendly, but usual caution to be observed at night.
Accommodation and Sleep
Taticoa desert (further north), is a good place to wild camp. There are also hot springs, but all sadly developed into resorts. Consider approaching English language schools to teach in return for board and food.