If you used up all the quests on your first class, they won't be there for future classes. You'll have your new classes' hunting logs, FATEs, levequests, and guildhests and dungeons when you get to those levels.

Each city/area has its own set of side quests, so if your new class is in a city that's new to you, there will be quests there. But with each city having multiple classes, it's not difficult to get into the same situation again.

What I've done is focus on only the main scenario quests on my first class, then try to split up the side quests in a given area between each of the classes with that area as its home. E.g., do a few quests on CNJ, leave a few for LNC and ARC.