A friend recently traveled to Mexico and really enjoyed her time there.
She flew into the city of Morelia from Dallas and then took a taxi to Patzcuaro, a smaller town on the lake of the same name. From there she was able to visit a few villages in the surrounding area.
She then made her way to Mexico City and San Juan Teotihuacan, which is about a half hour drive from Mexico City and is known for its Pyramid of the Sun and Pyramid of the Moon.
You can use local buses to get from Patzcuaro to the other villages surrounding the lake and from Patzcuaro to Mexico City. My friend used Uber to get from Mexico City out to Teotihuacan.
The smaller towns and villages are quite safe, but do use caution in the bigger cities, just as you would in any big city.