Well, with Google Maps you can download the map of Mexico City for free, but this only downloads the streets and map to your phone. If you want to have search and turn-by-turn navigation, you'd need data.
There are 3rd party apps that let you download more detailed maps and some have 'offline' turn-by-turn navigation, but those usually are paid apps. Not sure if the new HERE maps have a similar, free alternative though.
If you want to use Google, just zoom around the area that you'll be in (Mexico City in this case), hit the search button and scroll down to the bottom to where it says SAVE MAP TO USE OFFLINE. Now, this will save the map and streets to your phone, so you won't need data (just GPS) to see your position in a map, but you won't be able to get directions or search for a specific address unless you do have data (be it mobile data or WiFi, and the latter is very largely available for free around commercial areas of Mexico City).
When I was traveling once before I had free international data with T-Mobile, what I did was download the offline map to my phone, then plan my day either early in the morning or very late at night, let Google give me the directions using the hotel WiFi and either print them out or just save them to your phone and follow them while using your map offline. Sure, it won't alert you of your next turn, but at least you know where you are and you have a list of steps and streets to follow.