The Badlands is a desolate, rocky desert on the eastern coast of the Eastern Kingdoms; it's not only a good place to farm several useful materials for leveling up professions, but also a good area to level up in via the available quests. The ground route from Stormwind is a little convoluted though; there is no straight road leading directly to Badlands from Stormwind.
Ride out of Stormwind's main gate and head south to Goldshire. Take the road east and follow it into Redridge Mountains. Make sure to pick up the Goldshire and Eastvale Logging Camp flight points along the way.
Continue east on the road through Three Corners, then north over the bridge and past Lakeshire into Burning Steppes. Grab the flight point at Lakeshire along the way.
Ride north until the road washes out, then east to Flamestar Post. Then, head north into Blackrock Mountain. Pick up the flight points at Morgan's Vigil, Chiselgrip and Flamestar Post as you go.
Ride around the interior of Blackrock Mountain and exit it through the door on the northern side into Searing Gorge. You can go left or right inside the mountain, as both lead to the same place. Don't use any doors other than the one on the north, however: these lead to the Blackrock Spire and Blackrock Caverns instances.
Follow the road through Searing Gorge. This road winds considerably, and appears to fork at the Sea of Cinders. Follow the path to the left -- the right path isn't actually a road and leads you in the wrong direction. Along the way, pick up the flight point at Iron Summit.
Turn right at Thorium Advance when the road forks. This road will take you into Badlands, where you can begin your next adventure. Be sure to grab the flight point at Dragon's Mouth -- with this and the others picked up along the way, you should have a viable flight path between Stormwind and Badlands, making your next trip much easier.
Warnings:
- Traveling to Badlands from Stormwind requires passing through zones with higher level enemies than Badlands itself. If you're at a level appropriate for questing in Badlands, avoid enemies along the way wherever possible -- otherwise, you may be overwhelmed.