This post brought back a lot of memories.
I find flying into Mexico City more fascinating than any other city. It is equally impressive during the day or night. It's not just the sheer size of the city - Sao Paulo is pretty impressive too - but the flight plan that takes you over most of the city as you arrive. Sometimes the descent into the thick layer of smog is both fascinating and revolting.
As to the sounds of the city, I remember that we knew the coming and goings of the neighborhood based on what we could hear. Because doorbells often didn't work, people would announce themselves based on a particular sound. There was the man who drove up on his loud motorcycle and yelled "Las tortillas!!!" You had only a few minutes to grab a few pesos and run outside to buy them before he zoomed off. The milkman had his own particular whistle. Then there were the camoteros, who would ride around on their hybrid bicycle/oven that would emit a particular whistle. Another biker would be the guy who would sharpen knives by propping up his bicycle and pedaling to spin the sharpening stone. He had a little bell he would ring on his handlebars to alert everyone that sharpening services were being offered. The mailman would just tap on our gate. Our neighbors' friends would have their specific whistles to announce that they were there for a visit. A few would yell out the specific person they wanted to see. Then there were car horns that differed in timbre and people had their unique rhythm of honking. And I can't leave out the music - people sang without inhibition and car radios shared the music with the rest of the neighborhood. However chaotic all this may seem, the cacophony was woven into a complex symphony of place. All this may now just exist in my nostalgic thoughts, but I have no doubt that they have been replaced by a more contemporary version.
As to exploring neighborhoods. I don't think you are alone in the city when it comes to finding your movements constrained to a few areas. Involved I do think the difficulty of movement (traffic in particular) in the city is part of it. But Mexico is also very segregated by class (and by fear). Another issue is that a lot of the places you list, there isn't much that would draw an outsider. For example, Naucalpan was right next to where I used to live, but there really isn't much there for you to really explore. Unless you like small industrial parks and warehouses. Obviously, if you know someone there, they can take you to that special taco stand or show you that small plaza where you can hang out. But otherwise, you are the guero who got lost or came to gawk at how the "others" live.
My suggestion, though, is to find specific places to visit in different parts of the city. For example, go to the Sonora market and get a limpia or a sobada. Go to la Villa and sit and watch the pilgrims. If you want to go to Naucalpan, go visit the Basilica de los Remedios where people with illnesses go to pray for cures (there is also a cool statue of St. George slaying the dragon/devil - I could see that statue from my childhood window). Or just ride the length of a metro line, getting off at every other station. An interesting illustration of segregation is if you go to the south of the city, go from Jardines del Pedregal to Cuidad Universitaria to Colonia Santo Domingo. Three completely different worlds within a few kilometers.
But the city extends way beyond the DF. I couldn't tell you what to see in Cd. Neza or Ecatepec or Santa Fe, for that matter.
In any case, have fun and thanks for the trip into my memories...I spend enough time writing it, I thought I should post it here too. Why not?