there are a lot, really a lot, i have been in many places, but i can tell you the ones i know:
It's gorgeous, it's the capital¡¡¡¡ there are more than 20 millions, the zocalo is amazing, and the reforma avenue too. If you want to now the real mexican culture you have to start there.
Near from the city is the teotihuacan temples, "the city of the gods" one of the most known touristic places in mexico.
The "templo mayor" is another interesnting place you should go, its next to the zocalo.
-Guanajuato City: Wow it's my favorite, no doubt. It's so beautiful¡ really there are a lot of places to go¡¡¡¡ The whole city is gorgeous.
-San Miguel de Allende: It's a quite small town with a beautiful churches and a colonial enviroment. You can relax and feel in the 1960's. You'll love it.
- Dolores hidalgo: The birthplace of the mexican independence war. It's small and nice.
-Mineral de Pozos.
Well, all of them are really beautiful, I will name you the cities and look photos, it's better than words.
-Monarch Butterfly Biosphere Reserve
Jalisco (mariachi and tequila birthplace):
Baja California Sur:
-Cancun: An amazing beach, one of the necest in the world.
-Playa del Carmen
-Chichen-itzá: new wonder
-San cristobal de las casas
-Cascadas de Agua Azul
-Canon del Sumidero
-Popocatépetl and Iztaccíhuatl
-Barrancas del cobre
there are a lot more¡¡¡¡¡¡¡
according to the UNESCO HERITAGE SITES, mexico is one of the countries with more sites.
Historic Centre of Mexico City and Xochimilco
Historic Centre of Oaxaca and Archaeological Site of Monte Albán
Historic Centre of Puebla
Pre-Hispanic City and National Park of Palenque
Pre-Hispanic City of Teotihuacan
Historic Town of Guanajuato and Adjacent Mines
Pre-Hispanic City of Chichen-Itza
Historic Centre of Morelia
El Tajin, Pre-Hispanic City
Historic Centre of Zacatecas
Rock Paintings of the Sierra de San Francisco
Whale Sanctuary of El Vizcaino
Earliest 16th-Century Monasteries on the Slopes of Popocatepetl
Historic Monuments Zone of Querétaro
Pre-Hispanic Town of Uxmal
Hospicio Cabañas, Guadalajara
Archeological Zone of Paquimé, Casas Grandes
Historic Monuments Zone of Tlacotalpan
Archaeological Monuments Zone of Xochicalco
Historic Fortified Town of Campeche
Ancient Maya City of Calakmul, Campeche
Franciscan Missions in the Sierra Gorda of Querétaro
Luis Barragán House and Studio
Islands and Protected Areas of the Gulf of California
Agave Landscape and Ancient Industrial Facilities of Tequila
Central University City Campus of the Universidad Nacional Autónoma de México (UNAM)
Monarch Butterfly Biosphere Reserve
Protective town of San Miguel and the Sanctuary of Jesús Nazareno de Atotonilco
enjoy this video: