I have visited several states in Mexico: Sinaloa, Sonora, B.C., Chapas, Yucatan, Quintana Roo, CAmpeche and a few others.  The people were so warm and friendly.  They were very kind and patient with my poor Spanish.  I wondered from one small town to the next.  I could stop anyone on the street or road and ask for directions or advise on a place to stay.  Only in the DF was I approached by a well-dressed man wanting to show me around.  Being a Latin American Specialist, I asked him who the statue in the middle of town was, he did not know.  I told him Cristobol Colon.  He had no idea who that was.  So, I knew he was a con artist.  I got away as quickly as I could.  So, just like any big city or country, you just have to be careful.  As a tourist, you are always a target.  

I know about the Mariachis and would like to visit Tenochtitlan

That is a place too far for me to reach. 

Most of people who have visited Mexico say that was the most beautiful journey in their life. It is known for its ancient history, beautiful landscape, delicious food and nice people. 
I've heard that it's not recommended for individual tourists and it's better to go on an organised trip (for safety reasons).

I'd like to go to visit Mexico some day but I haven't planned it yet, so I can't say nothing about any particular tourists destinations there.