The best thing to do is when you start up, is to complete all the quests that the quest giver gave you. Doing so will usually ,after you completed most of the quests from him, make him give you a quest to go to another area with quest givers.
Also, it is a good idea to do all the quests from a quest giver as the quest rewards increase as you complete the quest chain.
Other than this follow the next quest giver thing, you can't pretty much do anything else but google the area you're in and see what quest givers are in there for A/H.
And other than that, the only thing left to do is to use a quest giver add-on(which should be the answer you were looking for). These are great as they show on your minimap AND map all the quest givers. You might find one similar to what I linked you to which you might find useful.
Also, maybe some quest givers won't be shown on map as you don't meet the level requirements for that quest. So if you pass by an NPC at lvl 10 he won't have any quests for you, but if you go again at lvl 15 he might have. Just a thing to keep in mind.
Ok, so I hope this helps.
P.S.:Quests and Leveling Add-ons