Mexico is a large country. Rather than just finding out if there is some sort of travel advisory for the country, look further into depth about the specific areas you plan to travel.
Any time you travel to a place where there are a lot of tourists, the biggest thing to be careful about are pickpockets targeting tourists who are busy reading maps and staring at the sites or staggering around drunk after too many cocktails with dinner and not noticing their wallet getting lifted.
My best advice is to keep copies of the front page of your passport at the hotel, and with someone back home that you can easily call to send it to the consulate's office if necessary. If you don't have a need for your US driver's license, leave that locked up in the hotel safe rather than carried with you, so if you do lose your passport, you have another form of photo ID that at least will help on the US side with recovering other documents lost when you return. And don't carry all your money in one place. Split it up, carry some in a wallet, some in a pocket, some in a money belt, leave some buried in your underwear in the hotel room (or some such non-obvious place...not sitting out in the front pocket of a suitcase where someone can quickly find it)...that way, if some gets stolen, you aren't out all the cash you had with you. Limit the number of credit cards you carry with you, and leave the rest home. None of this lowers your chance of being a target, but minimizes the damage should you become one, and makes it easier to just let someone take the cash you have if they mug you without worrying you're going to be stuck in a foreign country with no cash and no ID.