I would say just do fates and space out your leves so you don't run out of your allowance. While doing those you can either have a chocobo summoned to gain companion exp, or put yourself in a queue for dungeon entry, although if the DF pops while you are doing a leve then the leve will be failed because you have to leave the area. And yes complete hunting log objectives, and unlock the challenge log in upper limsa.