We were thinking maybe we had made a mistake scheduling a tour of the Sacred Valley outside of Cusco after our epic experience at Machu Picchu. Although it’s home to some of the most important architectural complexes of the Inca Empire, we wondered if it would be an anticlimactic disappointment?

Turns out we had nothing to worry about. Over the course of another long day in a van (once again in the last row 😕), we visited numerous sites featuring fascinating innovations by the Incas.

Our first stop was the ruins of Chinchero, a settlement that the Incas took over and expanded for use by the royal family before the Spanish arrived. The development is massive, covering over 100 acres, and highlights those terraces that seem to be everywhere in this part of the world.

Speaking of terraces, what we saw at Moray, the second location on our tour, was a remarkable example of Incan ingenuity. These amphitheater-like circles were actually laboratories to help them determine which...