http://ffxi.allakhazam.com/db/quests...fqtype=Mission
Every city has missions. I don't really remember how it works exactly, I just remember there's a cool progression of quests that are based on your level. Each tier you unlock new armors. To earn currency to buy them once unlocked, you have to slay with that city's buff on you which is given by the same guard who offers the items and quest (it's usually right next to the city gates) Sometimes the armors are better from another city, in which case you probably want to buy the pieces you need.
There are also a lot of random quests scattered throughout the cities. You should look up items. I ended up suiting myself up almost entirely with quests from cities and mission gear.