If you visit Blumenau in October, you have to check out the "Oktoberfest". It's the second biggest "Oktoberfest" in the world.
A good place for shopping, and also just to hang around, is the center Neumarkt on Rua Sete de Setembro. There are numerous shops, a multiplex cinema and a lot of food courts.
On Wednesday and Friday the "Observatorio" on Rua Antonio da Silva is worth a visit.