Cancun: Cancun is a city located in the southeastern part of Mexico, in the state of Quintana Roo, in the Yucatan peninsula. Cancun is one of the most famous destinations in Mexico, and one thing that you can see here is the Mayan ruins known as "El Rey."
Guadalajara: The city of Guadalajara is located in western Mexico. It is the capital of the state of Jalisco. One of the most important touristic attractions of this city is the Hospicio Cabañas.
Oaxaca: The city of Oxaca is located in the state of the same name. It is located in the Centro District in the Central Valleys region of the state, on the foothills of the Sierra Madre. One of the most important attractions of Oaxaca is the festival of the "Guelaguetza."
A Mexican artist that you could research would be Diego Rivera. Diego Rivera was born on December 8, 1886. He died on November 24, 1957. He belonged to several art movements, such as cubism and muralism. Two famous works by this artist are "Sueño de una Tarde Dominical en la Alameda Central" and "The History of Mexico." He is particularly valued in Mexico for his role in muralism, and for his collaborations with many artists of the time. He was also responsible for depicting much of the indigenous culture, traditions and art of Mexico. Personally, I think he was a very significant painter and a cultural icon, both because of his art and because of his marriage to Frida Kahlo.