Just do quests from the bulletin boards. And everyday there is something called a justice call and they'll announce a certain family of mobs that will give you 2x the exp if you complete the corresponding quest for them.
For example if they announce it for Beastkins, choose a bulletin board quest that asks you to kill any beastkin mob (ie. Cloudwisk Captain) and when you hand it in you'll receive 2x the exp and puzzle.
Be sure to pick up Fate quests as well. They give you slightly more exp than the white categories.
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