Photo: Dario Alpern, CC BY-SA 3.0 via Wikimedia Commons
This is the most convenient option. A free, short and underwhelming 30-minute tour, often in Spanish only, that involves driving around the dam on a bus preceded by a fifteen-minute video on the history and importance of the dam. A short lookout over the spillway provides the only photo opportunity.
The Itaipú dam operator also provides a number of tourist attractions and tours, including the Tati Yupi Biological Reserve, some of which require registration. And you will mostly always need some form of identification, so bring your passport. And for registrations require ahead of the tour, they will need names, ages and number of people.
The most convenient option is the simple Panoramic tour of the dam. However, it is worth booking a scheduled tour ahead, for a more interesting and different experience. You can still always do the regular tour.
Modelo Reducido de la Represa de Itaipú
A model of 1:100 of the dam.
Museo Tierra Guaraní (Itaipú) / Museo de la Tierra Guaraní and Zoológico Regional
A small museum mainly on the Guarani culture and the local wildlife. Descriptions in English and Spanish.
Cataratas del Monday
With a height of 45 m, 2 drops and 120 m width, the most impressive and beautiful waterfall in Paraguay. There are actually two (private) operators that grant access to the waterfall—compare prices! With the one further down the road you have a great view from above walking directly past the drop-off, but the elevator to the bottom costs a steep extra. Maybe not worth it, as you're too close to the falls directly in the mist.
On the other hand, the other operator (the one that comes first along the road from Ciudad del Este) has a platform at the bottom of the water, which can be reached by staircase (maybe a better overview from the bottom here). However, its top view is further apart from the waterfall and maybe not that spectacular.
Take a collectivo to the corner of Avenida Guarani/Avenida Monday and then walk to the entrances along Calle Aguaray.
Argentina–Brazil–Paraguay triple point
Paraguayan mark is quite far from the city, accessible by buses from the centre (Av. General Bernardino Caballero), take a bus labelled Tres Fronteras (destination, not the company name) by the bus company VICENTE A. MATIAUDA (red buses) and ask for La Balsa (the ferry), ask to get out in front of the huge gate. The viewpoint isn't as high up as the Brazilian and Argentine ones, but you'll have a head-on view of the Iguazú River gorge where it empties into the Paraná, just a few kilometers downstream from where it crashes down through the famous falls.
Tati Yupi Biological Reserve
One of several areas of Atlantic Forest not flooded by the Itaipu reservoir, now preserved by the Itaipu Binacional organization. Refugio Tati Yupi is the most accessible and has facilities for camping, picnicking, outdoor grills, horseback riding, and a small hospedaje with male and female dorms and a kitchen. The reserve has many small trails available for walking and wildlife includes birds, capuchin monkeys, armadillos, capibara and more.
To obtain authorization for a visit (self-guided), submit passport information and passengers online or at the Itaipu Visitor Center. Permission must be requested at least 1 day in advance of arrival and you will need to collect the set of papers to present to the guards for admittance. If visiting the dam before going to the reserve, permits can be requested in person in the office to the left of the zoo entrance. By stopping by in advance of touring the dam, zoo, and Guaraní museum permits can likely be collected before returning to Ciudad del Este at the end of the day.