The in-game maps have quest markers indicating the next quest in a zone.

If you have out-levelled the zone, make sure all quests are showing by clicking the magnifying glass on your mini-map and ticking the Trivial Quests box. This makes markers for quests show up on the world map, mini-map, and on NPCs, even if they are irrelevant for your character's level.

If you have Trivial Quests tracked, but still cannot see any zone quests on the map, but do not have the zone achievement, you should perform a user interface reset to resolve any possible display or interface issues.

Should you continue to have issues finding your quests, you may wish to use a third party resource or guide to find quests you may be missing in the zone, such as the Wowhead Quest Completion Tracker.