Visiting Mexico City - Safety and Precautions?

My wife and I are both 68 years old but we're quite active and steady on our feet. We're both Chinese. We plan to visit Mexico City in June. As we're Chinese, blending in with the crowd and not appearing as tourists would be out of the question. We take many photographs in all places we visit and we intend to do the same in Mexico City. I have a rather big Nikon DSLR camera and I'm wondering if I should bring this to Mexico City. We will only be out visiting tourist sites during the day and have no intention to be out at night. Our means of transport in the city will be by the Metro. If I do bring the camera I will be keeping it in a backpack which I will wear in the front of my body. I will only take the camera out for photography as and when I need to, otherwise it will be inside my backpack. Can anyone advise me with further precautions OR IS IT ADVISABLE TO LEAVE THE CAMERS BEHIND?

As yet, we haven't been to Mexico city, but have been to other parts of Mexico. No matter what part of Mexico we go too, we follow the same rules as we would at home when touring. I also carry a large Nikon camera. My carrying case looks like a back pack with room for another camera and all the gear that goes with the cameras. I carry a pocket digital Canon in my pocket when just roaming around a city where there are lots of people. People do come up to you and ask if you want your picture taken using your camera. If they do a runner with the pocket camera, your not out a great deal compared to the Nikon. If someone notices me with my Nikon, and asks to take a picture, I tell them my card is either full, or the battery is dead, then hand them the pocket camera. So far, I still have both cameras.
A couple of other rules to follow, do not flash a lot of money around, don't wear expensive jewelry, don't leave anything, such as bags, or cameras unattended, keep important papers, jewelry, passports etc locked up. Most hotel rooms have a safe for you to use. We carry a photo copy of our passports on us, just in case we're asked for identification. I carry one Visa card, and one debit card with me when away from my hotel, and always contact your bank and visa company before you travel to let them know you may be using your cards while in Mexico. If you don't, you could have your cards cancelled the first time you use them.

Have a nice holiday. Mexico is a beautiful place with beautiful people.