Pedro Juan Caballero
No matter what they tell you, you need to stamp your passport in Brazil and Paraguay, for entry/exit. The two offices are far away from each other. You can walk from one country to another, but if you're heding south, after 10 km they will check your passport.
Taxi drivers will help you driving to both places for R$ 15
P.S. Paraguay immigration closes at 10pm and opens at 8pm