Don't forget also the Challenge Log gives you exp and gil bonuses for completion, which resets every week on a Tuesday, as well as the Hunting Log for your class, although of course that's not repeatable.

Burning through FATEs and levequests is probably the best and most efficent way to level though, which if you're a DD class calling on your chocobo for healing (assuming you've put SP into the healer role) will be a big help.