I'll list the places I've used, the type of lead pet you face, and the availability of Stable Masters. If you want to know more about what pets are optimal for each, ask.
Wyrmrest Temple. Flyers/Aquatics. Your level 64 might have some aggro from the buzzards, but Stable Master is handy.
Crystalsong Forest. Critters. You can avoid mobs, but no stable master. You do need to run around a bit.
Mount Hyjal, Nordrasssil Inn. Flying/Magic. The lake behind the Inn is teeming with wild pets to battle, with few mobs, and handy SM nearby.
Pandaria, Halfhill. Nishi to Lucky Yi. Critters.
Pandaria, Mistfall and No-No. Aquatics. Handy SM at Mistfall. No mobs at No-No, but several people use that spot, and can soak up all the pets that spawn.
Dread Wastes, beside Gorespine. Like No-No, but with beasts as lead pets.
Draenor. Moonlit Shore, Shadowmoon. Ideal for a low-level, since there are no mobs and you can fly even at 60. Crabs as the lead pet. Horde do have to stay away from the edges where there are Alliance NPCs. No SM nearby, but you can fly.
Draenor. Frostfire Ridge. Icespine Hatchlings. If you have a Rotten Little Helper and Feline Familiar for the optimal strat, it goes very well. Like Moonlit Shore, you can fly, but mobs do run around, though sparsely.
There's a thread just below this viewtopic.php?f=3&t=16530
where someone is grinding in Zul'drak. I went there to check, and I can see that with the right lead pet, it goes very well, and if you can fly to the SM it could be very effective.