For levelling up quickly, I ground away at the leves. Once you get to level 10 in any class, the leves at Horizon (lv10) are by far the quickest and easiest, you only need to go just outside the gates and if you're efficient with skills, each will only take a couple of minutes.

I ran from level 8 to level 15 with my archer in about 45 minutes, same with ACN and I'll be doing the same on my CNJ tonight.

Fates are an amazing source of EXP, even if you only catch the end, it's worth joining in for the exp!