Final answer:
Quintana Roo is located on the eastern Yucatan Peninsula and is part of Mexico. It is a peripheral region with significant Mayan heritage and is known for tourist destinations like Cancún.
Step-by-step explanation:
The country that has Quintana Roo on the eastern Yucatan Peninsula is Mexico. Quintana Roo is one of Mexico's peripheral regions, primarily inhabited by people of Mayan ancestry and known for its little political or economic power. Despite this, the area has seen economic changes due to tourism; places like Cancún have become major tourist destinations, capitalizing on the rich Mayan heritage and beautiful coastal locations to attract visitors worldwide.