There are public toilets in Peru. I have been to Lima (the capital), Chiclayo, Cusco, and Huancayo. All had toilets that were exactly the same as here in the United States and were open to the public. In some really rural parts of Peru there are holes in the ground in sheds which are used as toilets. But for the most part everything is the same. In some areas they do not flush toilet paper as it clogs the pipes but they instead throw the toilet paper out in a trash can they keep in the bathroom. But in cities the bathrooms are generally the same. And in some areas you have to pay to use the restroom, but not all over.
http://www.adventure-life.com/articles/peru-adventures-32.php