Brazilian side of the falls (10km, half-day). The Parque Nacional do Iguaçu on the Brazilian side offers the panoramic view across the full width of the falls. An easy taxi or tour excursion; check Brazilian visa requirements for your nationality before going.
Itaipu Dam (12km south of Foz do Iguaçu, Brazil). The Itaipu hydroelectric dam on the Brazil-Paraguay border was the world's largest power station by generating capacity from its completion until 2012, when the Three Gorges Dam surpassed it. Daily tours of the dam structure and control facilities run from both the Brazilian and Paraguayan sides; the engineering scale is genuinely impressive. Allow a half-day from Puerto Iguazú.
Ciudad del Este, Paraguay (across the Friendship Bridge from Foz do Iguaçu). Paraguay's second city is a chaotic, energetic border market town with duty-free electronics, clothing, and goods drawn from across Asia and South America. The crossing involves two border controls and is best done by taxi. The experience is more interesting than the shopping — a glimpse into a very different kind of South American city.