Quickest way to level

[Garlyle]

Your daily Low Level Duty Roulette is the best source of EXP, once per day. Guildhest Roulette once per day also helps a bit.

Past that... doing your most recently-available dungeon, doing levequests, doing FATEs, are all sort of even-ish; and of course if you haven't exhausted them yet you've got quests too. If you mix up a variety of them all you can also score your Challenge Log bonuses, which are additional large chunks of EXP. Once you hit 41(?), the Beast Tribes start opening up with extra daily quests you can take.

[Niwashi]

Your daily Low Level Duty Roulette is the best source of EXP, once per day.

And for tank (or occasionally healer) classes, it can be more than once per day. The big XP bonus that's available to all classes is a once-a-day thing, but the most-needed-class bonus is available however many times you want to run it. If leveling multiple classes, I'd run DR once as DPS, so that class gets the once-a-day bonus, and then run it again as a tank or healer, whichever is currently getting the most-needed-class bonus.