I second the recommendation to go to the Templo Mayor.  Look at the excavation
of the Templo Mayor and then go to the excellent adjacent museum.  Neither
of these is that large ... very good if you only have one day.  I only had
three days in Mexico City and this was first on my list.
The National Palace is basically next door and you can see some wonderful
Diego Rivera murals there, if you like.
I agree that the National Museum of Anthropology has magnificent artifacts.
If you like Mesoamerican archeology you should not miss this.  Stick to
the first floor if you don't have much time.
Others have recommended the Frida Kahlo Museum and it is definitely
worth going to.  However, if you only have one day you might not want
to spend the time it takes to get there unless you are a real fan of Kahlo.

For the person going to Oaxaca, do not miss the ruins of Monte Alban (Mitla too
if you have the time.)  There are also a couple of museums in Oaxaca city that
have archeological collections (sorry, I can't remember their names right now.)