People ask me this question all the time. The simple answer is, "I dont know".
The more complicated answer is, depending on your race, job/sub-job, abilities, nation, and luck the best place for you to level will vary. I'm a Galkan MNK from Windhurst. I know that levels 1-10 I spent most of my time in East and West Sarutaburuta with some moonlighting in Giddeus. Past 10, I spent a lot of time in Tahrongi Canyon. But I could always take and dish out a lot of damage with no real ability to heal or avoid poison, so where I went would likely differ from where a Taru WHM might go.
Typically, your maps should be your guide. The areas immediately surrounding your hometown will have light stuff that you can take levels 1-10. The farther you move away from your hometown, the nastier things become. Beyond that, certain areas will have certain creatures more dangerous to certain races/jobs. The best advice is to scout places out and never attack until you've properly identified an enemy.