Northen Thanalan is definitely the best option for your level, but I understand most FATEs aren't soloable. You can do most of them with your chocobo and at least one more person (: Like others said, put up a Party Finder for them. A lot of times people are not really planning on doing FATEs or leveling at all, but when they see someone else is doing it, they hop in! Also mentioned before, it's VERY helpful to make sure you do the Challenge Log every week. It gives tons of EXP for really silly stuff, like doing a certain amount of Levequests or Guildhests! It helped me out a lot to level the last couple battle classes I had left.

But being honest, the best way to level up is to have someone else with you. It'll be a lot more fun and fast with friends~ (: Or try to make friends with people on the parties you get for FATEs. That's how I met most of my in-game friends