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As a Druid you will have a cat form that goes faster than run speed, I think it's 40% faster than run speed, but I'm not sure what level as I don't play a Druid.
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20th Level I think, but like Edward I do not play Druids.
Additionally, as a Paladin and a Warlock instead of forking out all that gold, you get a spell at 40th level that lets you summon a mount.
Final thought, had you chosen a Draenei Shaman, at 20th level, you could change to 'travel form' which is a wolf that moves at 40% speed increase.
All in all, the players in that immense world around you, all walked everywhere until 40th level. I groaned and groaned on my main until I hit 40th and got a mount, but since then, 1st to 40th level really goes by quite quickly.
The two runs I hate to make though would have to be from Menethil Bay, in the Wetlands to Iron Forge, (the Night Elf run) and the run from the top of STV to the bottom end into Booty Bay.
Hope that helps. Just rest assured knowing, everyone around you had to run til 40th and once you get a mount, you will look at the walkers of the world a little differently.
Bo