Why when asked what the fastest way is are people excluding the fastest way from their replies? Fates, leves, hunting and challenge logs are the backup methods for leveling when you don't have any quests available.

But Starkman mentioned having "done all the quests in Gridania, but done nothing level 15 or below in any of the other areas." That means all the La Noscean sidequests that you'd use getting to level 15 are still available. And they're by far the fastest as well as most interesting way to level up a secondary class. (As an added benefit, they also provide a fair amount of low-level gear if you no longer have the gear you used as a low-level lancer.)

If you're intending to stick exclusively with Dragoon, use all the low level quests in Limsa Lominsa and La Noscea to level your Marauder. If you're planning on eventually branching out and picking up all the other classes as well, you may want to spread the quests out, using around half of them on MRD and later having the rest available to level Arcanist. In that case, you might add in the hunting log and maybe a FATE or two to fill in the gaps.