Wow.

[Garlyle]

The best ways to level are generally irrelevant of the level of regular monsters.

First and foremost, the best EXP comes from dungeons. As you should have more than one dungeon available, doing your Roulette: Low Level each day grants you a massive EXP Bonus, on top of the already high EXP from dungeons - you should net about two levels just from that!

Past that, sidequests generally are for the level that you reach the area in on your main quest - for instance, when you head to Camp Drybone at around level 18, the sidequests in the Camp Drybone area are going to be around level 18-20. These also are around the level of the FATEs that will spawn in the area. Now, frequently a single zone may contain additional sectors that have differening level ranges, but as a general rule, the closer it is to wherever your main quest line is taking you, the more level relevant it will be.

For levelling alternate classes, you may no longer have sidequests available, in which case I recommend FATEs in...:
1-12: Do your hunting logs, class quests, and a couple FATEs in the areas your hunting logs send you to.
13-19-ish: Western La Noscea typically
20-30: South Shroud, I think it is?
31-40: Coerthas Central Highlands
41-45-ish: Mor Dhona
46+: Northern Thanalan

Mix in dungeon queues while you're doing those, of course.