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Why would you want to go to Gadgetzan ...
High level Trainers and Vendors.
One of the three Neutral Auction House where items can be sold between factions.
A Bank.
Hanging out (or fighting) with the Alliance.
Arena masters.
This is how to get from the Horde town of Crossroads in the Barrens to the Neutral city of Gadgetzan near the southern tip of Kalimdor:
Take the road south from Crossroads to the southern Barrens past Razorfen Kraul which is on the west side of the road) until you reach the Great Lift into Thousand Needles.
Once in Thousand Needles, follow the road south for a short distance and then follow the road southeast pastFreewind Post. You can go through this area safely around level 25+. Don't forget to get the flight path at Freewind Post, too.
Continue southeast until you enter the Shimmering Flats. The mobs in this area are around level 30, so be prepared to avoid them (pretty easy) or fight.
Go roughly south (or follow the faint road marked by totems) in the Shimmering Flats until you reach a rocky hillside path marked by torch poles and follow it up and over.
You should enter the Tanaris Desert and immediately see Gadgetzan as you come down the hillside.
Alternate, but probably harder method :
Take the road south from Crossroads to the southern Barrens, but go east (left) after the Field of Giants. This will take you into Dustwallow Marsh.
Once you've entered Dustwallow Marsh on the road, take the second left (north) until the road starts going due north. You may want to detour to Brackenwall Village and get the flight path.
Once the road starts going due north, head directly east to the northwestern tip of Dustwallow Bay. You may have to dodge some Alliance Sentry Point Guards, crocolisks, raptors or spiders until you get to the water.
Once in the water, swim southeast through the bay until you can swim south around the tip of the peninsula south of Theramore Isle. You may have to dodge some Muckshell Clackers (or Muckshell Snapclaws; both crab-like things) or Young Murk Threshers (or Murk Threshers; both loch ness monster like things). If you keep a sharp eye, you can swim around or outswim them.
Once you've gotten to the east coast of the peninsula south of Theramore Isle, you just swim along the coast until you reach Steamwheedle Port on the northeast coast of Tanaris.
From Steamwheedle Port, its just a short run west on the road to Gadgetzan past the Noonshade Ruins. You may have to dodge an occasional Blisterpaw Hyena, but that's it.