National Cathedral en Zócalo
When you are facing the National Cathedral, there are two entrances. There's one on the right, and there's one no the left. The one on the right is for a smaller chapel. Check it out. It's cool. But some people get confused and think that's it, and they leave, and they don't realize, "Oh, no, to the left is this huge chapel", which is actually the biggest church in the Western hemisphere. It is just like the Vatican, in terms of grandeur. It is overwhelming marble, and sculptures, and Baroque art every single place that you look. I love it!
The National Cathedral is open a little later than the National Palace. I suggest going to the Cathedral after going to the National Palace, which is half a block away.
National Cathedral: They have a mass at 7 PM, which means at 6 PM they start to close down the public area, so if you're not going to be worshiping, you won't be allowed to see the full thing. So make sure that you get there I would say probably before 5 PM. Now, what's really cool is if you do stay for the Mass, you can hear the organ playing, which is this gigantic,building-sized organ. So, if you're interested in that, stay for the Mass at 7 PM.