This weekend when my priest got 60 and flying, I decided to see how many masters I could run.
I began by asking for a port to New Dal. No guildies were on to do it, so I offered 100g to a mage and went to the tower in Stormwind. She gave me the port at no cost.
Pandaria- Definitely worth it. Fly HIGH. There are some birds in a few zones, but if you are high you can still hit all 11 masters/elementals. Each drops a bag of goodies with a chance for battle pets and bandages and other tokens. I have all the fights scripted there and win. Some you can do with lvl 1 pets, others have back line damage and you have to do higher battle pets.
Warlords- I took my level 60, flew from Pandaria to Timeless Isle. I took my water strider around the coast on the north side until I got to the underwater cave. I did pick up some agro from the ship, but it dropped off as I continued to move to the cave. Sat on the chair, clicked the fire, and my level 60 was in Draenor. First lesson- do not do the Gorgrond master. There are bees that fly around the guy there, and you will get killed. I could do all of the rest, which I did in a big clockwise circuit. These guys give you the old outdated pet currency, which is useful to buy a few pets from the vendor. Overall this was not worth the bother at base level 60 flying. You can do it if you are determined, but the payoff is not that great.
Northrend/Outland- both of these zones work for a 60, with little problem. They are separated by quite a bit, but if you have mining and gathering, you can rack up some gold by picking as you fly between masters. If you are time limited, stick to Pandaria. If you have more time, these can add up.
Eastern Kingdom- as Alliance, most of the pet masters are here. Flights are pretty short, and this is a good way to take level 1 pets to something that can take a punch. You get about a level if you run them, and there are no real rewards other than xp for doing so. I do go into Twilight Highlands when I do this, and that master is pretty safe at 60
Kalimidor- Not worth it for Alliance. Most of the masters are for Horde.
Oh, and even though reset is at 11am Eastern for Anvilmar, if you do quests after around 10am or so they will not reset. So if you are getting close to reset, do Pandaria first, then the other stuff. By around 10am I had most of Eastern Kingdom done, and by 11am I had Pandaria done, but the Pandarian quests did not reset, and only the Eastern Kingdom guys I did first had reset.