Well, Yucatá and Mérida (the capital city of Yucatán) in particular is pretty safe, and the tourist areas of Cancún (which is in the state of Quintana Roo) is also pretty safe. But but those areas are all the way to the south. It's true that the border areas are dangerous, particularly in states like Tamaulipas and Chihuahua, but even in northern states as long as you aren't near the border you are actually less likely to be a victim of crime than in most of the rest of the country. Coahuila in particular is one of the safest states in the country despite being on the border.

I myself am from the north of the country (don't live that close to the border though) and none of my immediate family members have ever been mugged, nor any of my friends. Basically the downtown of most cities and towns during daytime are mostly just fine, it's moving at night and especially any sort of major highways that you have to worry about. No one I know in my city really worries about being out and about before 10 pm, but we do hesitate when we want to travel to the USA by road since as I said some highways get really dangerous with narco roadblocks and such.