The falls are the whole point of Puerto Iguazú — everything else in town is secondary. Both sides of the falls are worth visiting: the Argentine side (Parque Nacional Iguazú) is the more immersive, putting you on elevated walkways directly over the cascades and close enough to feel the spray; the Brazilian side offers the classic panoramic view across the full width of the falls that you recognise from photographs.
Allow at least two days. One day for the Argentine side is a minimum — the Garganta del Diablo alone justifies the trip, and the Upper and Lower circuits take most of a day between them. The Brazilian side is an easy half-day excursion. If you have a third day, the Itaipu Dam and a wander around Foz do Iguaçu on the Brazilian side make a worthwhile addition.