Well, what I really know is about Colombia, where I am from. If you’d like to go there, and you should… choosing a city is up to what you want to do.
Bogota is the capital city and it is beautiful and you can do whatever you want there, this city never sleeps and has the greatest places in the world… you will see. In Bogota you can find a job as an Industrial Designer in any field, however what you can find easier is in the furniture design field, events design, P.O.P, Stands, a little bit of Fashion design and a lot of graphic design (web, print, multimedia, TV, etc…).
Cali, my hometown is a very hot city and it is also beautiful, however at the moment is kind of disturbing because theres a lot of construction going on with the new transport system, and the city has gone through a lot of problems with politicians in the past few years. But of course you have to go there at least for 2 weeks to party like we do ) In Cali you can find Furniture Design but not to much, P.O.P a alot!, events and stands design and graphic design.
Medellin, is another big city in Colombia with a wonderful weather and wonderful people as well. This city has maybe the best Web/Multimedia and Information Design industry in Colombia, great firms there. and of course they have the common fields of furniture, P.O.P, etc… and some product design but I would not rely on finding a job designing products such as white electronics and stuff.
Cartagena… well I dont think you will find a job there! but is the most beautiful city in colombia, the beaches and the people… and the architecture! and the history! damn I love it!
In Brazil I know they do have pruduct design and a very big furniture design industry.
Well, thats all I can tell you, I hope you finde a good job and have fun in this beautiful continent full of great and friendly people…