Cities are special safe zones in which you don't find hostile creatures, FATEs, and other combat-oriented activity. You can teleport throughout a city using the Aethernet - an interconnected system of smaller attuning crystals. Cities are occasionally decorated for special events such as Valentione's Day and Starlight Celebration.
The character starts at Limsa Lominsa, Gridania, or Ul'dah and develops their classes and jobs, as well as unlocking various systems, by traveling to each of the cities. The main scenario quest will take players to all of the cities at different steps, and usually requires revisiting the main cities every so often. Large portion of every character's story plays in the capital cities.
There are a few other special zones. They work similarly to cities, but they serve as the staging points for specific game modes or activities.