My visit to Paraguay was much more of the brief pass through variety than a nice extended look at the country and its people. It just so happens that if you're around Iguazu Falls, it's pretty easy to make a side trip over to the border city of Ciudad del Este, although don't expect there to be a ton of stuff to see or do there.
I arranged a taxi tour that also took care of immigration at each checkpoint - I didn't even have to get out of the car! While immigration is pretty lax between Brazil and Paraguay, it's still worth following proper procedures to stay on the right side of the law.
The city itself is largely a commercial shopping district, filled with black market goods. The costs here are much lower than in neighboring Brazil or Argentina, so it's a popular spot to pick up that fake purse, cheap clothes or new toy for your kid. I didn't visit for shopping, though I did end up with a Paraguayan yerba mate cup as a souvenir.