Puebla is the state capital of the Free and Sovereign State of Puebla. It is a UNESCO heritage site, and on the Mexican citizenship test, the answer to the question which Mexican city is known for its colonial buildings. It's very beautiful and one of my favourite Mexican cities. Additionally, it's known as the place where the Mexicans won the Battle of Puebla on Cinco de Mayo, when Napoleon III of France attempted to install an Austrian archduke as Mexico's emperor. There's also something something revolution. When it comes to food, it also claims to be the origin of mole and the independence day favourite chile nogada.
From Mexico City, it's around 2 hours by bus from the TAPO station. The CAPU bus terminal is not close to the city centre, but the airport is even farther away. CAPU is connected to the centre by bus.