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There is no flying in Draenor, but there are Challenge Mode gold teleports, portals via the Mage Tower in your Garrison, portals in Ashran faction hubs, Garrison bodyguards, reputation items, and Engineering Wormholes that can help you get around.
The easiest way to get to Draenor if your Garrison Hearthstone is on cooldown is to take a portal from the Stormwind Keep or Warchief's Hold to Stormshield or Warspear.
For the map dots, green = reputation, red = garrison, blue = challenge mode, yellow = mage port.
Much has been made of the lack of flying mounts in Warlords of Draenor, so we're taking a look at teleports and portals that can help you get around Draenor quickly. Also keep in mind that the Level 3 Stables can increase your mount speed in Draenor by 20%!
Challenge Modes
Achieving gold for each Warlords of Draenor Challenge Mode unlocks a teleport to that dungeon.
Auchindoun: Gold: Teleport: Auchindoun in Talador.
Garrison Hearthstone is a special additional Hearthstone you get from Establish Your Garrison/ Establish Your Garrison. This does not share a cooldown with your main Hearthstone.
Completing Seaman rewards Admiral's Compass, which lets you port to the Shipyard every 4 hours and does not share a cooldown with your other Garrison hearthstone.
With a Level 3 Mage Tower / Spirit Lodge, you can create Ogre Waygates around Draenor, which are one-way portals from your Garrison to a location in Draenor. There are seven ogre waygates in Draenor, and you activate them by collecting 25 Ogre Waystone, visiting your preferred location, and clicking on the gate:
Gorgrond at 58.0, 34.5 by Blackrock Foundry
Nagrand at 32.2, 46.2 by the Ancestral Grounds
Spires of Arak at 54.6, 51.6 by Veil Zekk.
Shadowmoon Valley at 50.5, 35.6 by Embaari Village
Talador at 55.1, 46.0.
Frostfire Ridge at 61.5, 45.6 by The Crackling Plains.
Tanaan Jungle at 53.5, 58.4 (requires lvl 3 Mage Tower).
With a level 3 Garrison, you unlock a tower that contains a port to Stormshield or Warspear.
Home Away from Home is a port to your Garrison Outpost in Spires of Arak if you choose the Brewery option.
Completing the "Iron Siegeworks" part of the Garrison Campaign rewards a mole machine that ports you to your Gorgrond outpost--Beastwatch or Highpass.
Finally, some Level 3 Bodyguard followers have portal and summoning perks.
Defender Illona and Aeda Brightdawn can summon party members at max friendship: Aeda Perk: Ritual of Summoning, Illona Perk: Guiding Light
Delvar and Vivianne open up portals to your Garrison at max friendship: Vivianne Perk: Portal: Garrison and Delvar Perk: Death Gate.
Portals
Mages can open portals to the capital cities Portal: Stormshield and Portal: Warspear.
Major Azeroth cities have portals in Stormshield and Warspear.
The Alliance can port to Darnassus, Stormwind, and Ironforge from Stormshield.
The Horde can port to Thunder Bluff, Orgrimmar, and Undercity from Warspear.
Players can port between Stormshield and Warspear and Tanaan Jungle when they have unlocked Tanaan Jungle.
Players can port from the Stormwind Keep and Warchief's Hall to Stormshield and Warspear respectively.
Professions
Engineers have a new Wormhole! Wormhole Centrifuge is on a four hour cooldown and lets you choose what zone you wanted to be ported to. Make sure you have Parachute Cloak, Goblin Glider Kit, or another slow fall because many of these options will port you high up in the air.
Wormhole Centrifuge Binds when used, requires Engineering 500, and takes 50 Gearspring Parts.
Reputation
Relic of Karabor: Requires Revered with Council of Exarchs. Teleports Alliance user to Path of Light, the equivalent of the Black Temple.
Bladespire Relic: Requires Revered with Frostwolf Orcs. Teleports Horde user to Bladespire Fortress in Frostfire Ridge.