First of all, if you're a new player then you should have no shortage of story and side quests to reach level 15. There's really no need to do leves or guildhests. Hunting logs and FATEs, you can do as you go, but no need to farm FATES if you're below level 15.

Second, I levelled my Black Mage primarily through dungeons. I've never gotten queue times over an hour. 40 minutes at most. If you haven't done so, then be sure to tick the other languages (JEDF) to make queue times faster. If you have run out of leves then I suggest levelling a crafting or gathering class to pass the time. You'll be able to make some gear for yourself as you level and maybe make some money in the process.

Next, you also have to consider the alternative. Look back to pacth 2.1. Nobody did FATEs. The maps were barren.