FATE grinding is a thing, and if you have a tank or healer friend, you can run dungeons as well.
Just follow this advice:
Eat food. Any food. You just want the exp bonus so even mineral water is fine.
Get in an FC that throws up the Heat of Battle free company bonus.
Make friends. Queue together.
Hunting Log. The ROG one is REALLY easy and convenient.
Challenge Log.
Also, you can do levequests for exp as well. It's not perfect but there's a trick you can do to make it faster: have a high level friend solo the levequest, which should be as high as you can possibly get, and then you turn it in. Rinse, repeat.