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There is one Capital city in Outland, Shattrath, which is a neutral city open to both Horde and Alliance.
To get there, you can either cross Hellfire directly west to Zangarmarsh and then follow the road south to Terokkar (you cannot miss the city when going this route, it's very obvious), or you can take the southern exit from Hellfire into Terokkar Forest, and then turning west when the road does.
There are two Inns in Shattrath, one on Scryer's Tier and one on Aldor Rise. On your first visit you can set you hearthstone at whichever you wish as you will be neutral with both, but once you choose either the Scryers Faction or the Aldor Faction (the other will not like you anymore), you should set your hearthstone to the matching inn.