By constantly doing quests, you will experience a very different game than if you just level through pure grinding. You'll be out there making a contribution towards the Alliance or the Horde. Doing these quests takes you through the heart of the game's story AND provides the fastest rate of experience. Have fun in World of Warcraft and enjoy developing your hero - your adventures will gain you great reputation amongst the land.
Isle of Quel'Danas: Special mention. At lvl 70 you can start doing the dailies here. Despite not being able to fly, the quest density is VERY high. I recommend hitting this every reset if you spend more than 24 hours REAL time(not /played)in the 70-80 level range. In fact, if you're doing a monk and only logging in once each day anyway, IQD WILL be your best exp/h for this level range. If you're going to hit the island more than once, it's probably worthwhile to change your hearth to the Shrine in MoP at this point to facilitate faster travel back and forth.
Fully rested experience (this is the blue color your experience bar takes instead of purple) grants 200% more experience per kill. Quest experience does not work the same as mob experience. Instead of just using the rested bonus, quest experience pushes the bar further upwards extending the rested bonus. Say if half your experience bar is blue. If you turn in 10 quests all at one the normal experience from them all could boost a character a full level. Unlike mobs where the experience gain will use up said bonus - the quests merely 'push' the bar further. Doing this could net you a level and still have the 200% bonus for mob kills applying to milk the rest bonus.
Something to keep in mind as well is that this will make enchanting materials more valuable, since it is likely most players will now simply scrap their boe greens instead of getting them disenchanted. Also redundant dungeon/raid gear can be scrapped rather than traded to the (guild) enchanter in the run. Less stuff gets disenchanted, meaning there will be less ecnhanting materials, meaning their value will rise. All the more reason to DE rather than scrap as an ecnhanter.