The Town and Neighborhoods of Mexico City are what make any trip to Mexico City so special. In and out of the urban, Mexico is famous for its small towns, very often designed with exactly the same set of standards.
What that means is that you can visit any and almost all of them with a pretty good idea of what to expect.
Some pueblitos have largely been subsumed into the larger city. While they may not constitute a full "day trip," they will greet you in a similar fashion. Visit a museum and walk the surrounding streets, then settle in for a coffee on the side of the plaza.
Others, like the far-flung villages in Milpa Alta , or Cuajimalpa , can make you think you've really traveled far, even if you're still in Mexico City. They are all used to welcoming visitors and the residents know how charming these little places can be.
Mexico City's neighborhoods and little towns can take all sorts of forms and each one brings a surprise. Don't be surprised if you end up wanting to visit them all.