Corumba lies on the Rio Paraguai, which separates Brazil from Bolivia. The border itself is a short bus ride away. You'll probably arrive at the bus station which is a 20 minute walk or a short taxi ride away.
Unlike many South American frontier towns Corumba doesn't feel unsafe to walk around in, even at night.
Most of the towns action is around the Delamar thoroughfare. This is where the majority of Corumba hostels and hotels are located. Many have an internet cafe as the front of house. Also near this street are a good selection of juice bars, fast food, restaurants (including a few comida por kilo joints), and internet cafes.
Most travelers come here en route to/from Bolivia or to the Pantanal, which is under two hours by bus away. Accommodation is not cheap, although its a' bit cheaper than larger Brazilian towns.
There is not much to do in Corumba other than to get ready for the next stage of your journey, but it's a lot more pleasant to stay here than on the Bolivian side in Quijarro (however Quijarro is much cheaper).
Grab a beer and go watch the sun the sun go down from a wall overlooking the river before heading to your next destination.
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