Illuvias - called the City of Magic, the Citadel of Mages, the Holy Root. It is home to the greatest and grandest magic library in the world, and also host to the most renowned of all magical academies. Stories say that of the mage students that set out for the city, only 1% reach their destination. It is said that finding and reaching the city safely is enough to prove yourself a worthy mage, and more than enough to gain you entry. (Entry into the Academy is not garunteed, of course.)
The mages take great pride in living in a inhospitable environment. They believe it is proof of their mastery over nature. Terrances carved into the sides of the volcanos host all sorts of farms. Water is drawn from common fountains, pools, wells, or faucets (all powered by magic, of course). The lava may seem free flowing, but in most areas a protective barrier prevents it from splashing up and causing harm. The lava itself is used for heating, though the mages also collect solar power from the sun.
The lower areas are home to residential areas and workshops. The middle levels are home to the most improtant parts of the city. The upper levels are home to residentla areas and workshops, as well as some large open air parks/stadiums. Magical stairways and platforms as well as various enchanted things (brooms, buckets, etc) or magical animals also provide transportation. There is something akin to a magical tram system (a la Ba Sing Se from Avatar) to transfer materials between the levels of the city.
A giant World Tree grows suspended in mid-air in the volcano, and the mages take great pride in it. The presence of the World Tree provides enough mana for all sorts of magical experiments and spells, not to mention sustinence. The city itself is built around, and on top of the Tree.
Location: Located far to the West, in a volcanic mountain range. The city itself is located within a live volcano. The surrounding area is a still-active caldera and has a host of things like gysers, lava floes, forests, burnt lands, wastescapes juxtaposing grass plains and desserts. The area also features various magical artefacts - leftovers from great spells that include odd things such as floating crystals, fossiled rivers and illusions. The pressence of a World Tree means that the number of mythical/magical beasts is high in the vicinity.
Population: ~10,000, give or take a few thousand. The surrounding area is also home to dragons, and several live within the city - tending to the tree and sharing knowledge with the mages.
Government: A meritocracy. The head of the city is also the elected head of the Citadel of Mages, rather it can be said the High Council of the Citadel of Mages oversees the city. General elections don't exist. Instead, rank and position can be won either through the yearly Mage Trials or through "exceptional magical talent" aka discovery or proof of talent. The Tree Priests, those mages who are dedicated to the cultivation, preservation, and betterment of the World Tree, technically occupy the highest place on the social heirarchy but they have little to now power since they're too busy taking care of the tree.
Commerce: The mages create a bunch of things - from spells to potions to enchanted wears - and welcome people to come buy them. (For mages, it is the creation of the item itself that holds value.) Merchants and warriors that can make it to the city are welcome to visit the shops. But the mages themselves don't take my perrogative in selling their wares since they have no reason too. As a self-sustaining community of plenty, they have no need for trade.
Beliefs: magic magic magic magic talent talent talent talent genius genius genius genius also, o u poor lil mortals w/o magic