If you're traveling inside mexico city dont bring your laptop and leave it on the safebox of your room, you wont be able yo use it anywhere and you CAN be mugged, i've been living there for 7 years and never carry nothing more than muy cellphone, my wallet ando my keys and a small camera sometimes, as someone else stated, stay not classy and ffs dont use obscure glasses everywhere unless you're on a really Sunny plac like Teotihuacan or the Puebla Center, makes you look like a douche and people would want to scam you into buying overpriced shit.
Another place to visit that i recommend very often Is Guanajuato, lived there contracted by the local university, wich Is one of the main attractions of the City, there are a whole Lots of museums, markets of sweets and a plethora of good restaurants, also the nightlife Is very energetic on thursdays, be sure to hit the Center if you go there, it's a mountain embeded City, funded by old miners (not working mines anymore) so there are a lot of historic and mine museums also a mummy museum. Another plus for this Is that the highways are fast and safe. You can arrive in a 5 h bustrip from cdmx.
The west coast of México from Chiapas up to Jalisco Is safe with the notable exception of the Michoacán coast, but i dont think youll be abducted even if you go as a tourist to the principal attractions this state has to Offer, it's like a great lakes zone within the mountains, dont go to beaches there theyre awful.
Like other anon said go to Oaxaca for all the experience plus 5 hours by car everyday, the state Is huge and bad conected. The City Is beautiful.
Chiapas Is a big contendant for visiting but it's far and Costly to get to, even far than Oaxaca and gto, i recommend a plane for this but the experience Is worth it, There's a huuuge sailable canyon, cañón del Sumidero that i recommend cheking out, also Is a state with variety un it's climate from mountains in San Cristóbal to coastlike in Chiapa de Corzo.