Mexico City is one of the largest and busiest cities in the world. It is the heart of the country and center for everything modern and traditional for the rich and the poor. Visit for example the Zocalo and have some really nice food.
Chichen Itza is probably the most famous archeological site in Mexico. The main temple was the way to the Sun for the ancient Aztecs.
Oaxaca is a culturally very rich, but touristy city in central Mexico. It’s known for its colonial buildings, many of which are made from green volcanic stone. There are also many colorful murals.
Palenque features some very ancient and well-maintained Aztec ruins.
Playa del Carmen is located on the Riviera Maya very close to Cancun with lots of hotels, restaurants and tourists. The water is clean and great for swimming, snorkeling and diving.
San Cristóbal de las Casas is a town in the Central Highlands region of Chiapas. The city, especially the historic center, has maintained its Spanish colonial layout, with narrow cobblestone streets, roofs covered in red clay tile and wrought iron balconies with flowers.
Uxmal is an ancient Maya city in Mexico. It is considered one of the most important archaeological sites of Maya culture, along with Palenque, Chichen Itza and Tikal (in Guatemala).
Cancun and Playa del Carmen are famous beach resorts on the Riviera Maya with the best hotels, bars and a lot of US-Americans.