I just got lvl 60 on my warrior alt and it took just under 11 game play days. (type /played fyi)

The way i got it so fast was LOTS of soloing. I barely grouped and when I did it was just for tough elite quests or instance quests. So if your not a grinder and wanna get lvls quick just do quest after quest after quest by yourself.

I'm not saying grouping is bad at all... its just if u want the lvls... solo is the way.

The areas i went were (these are in order)
Dun morough
Elwynn Forest
Westfall
Loch Modan
Redridge
Duskwood
Wetlands
Hillsbrad
Arathi
Thousand Needles
Desolace
Stranglethorn Vale (left and came back alot after some lvls) 30-45 area
Dustwallow
Feralas
Tanaris
Hinterlands
Blasted Lands
Un'Goro
Felwood
Western Plaguelands
Winterspring
Eastern Plaguelands

Now I didn't stay in these areas till they were completly done because u have to do some jumping back and forth but this was pretty much the order.
I made sure I visited every town/camp and got all the quests I could.

Also went to Deadmines around 16-20, stockades 25 ish, Scarlet monastary 34+, Uldaman at 42+, Zul Farrak at 45+, Temple 50+, then when u get in the higher 50s u can do the rest.