EDIT: Sorry, apparently the portal does not unphase for the Horde. This is alliance only!
Bug: You can use the opposite factions portal in Twilight Highlands to access the opposite faction's main city easily.
I can't be sure which quest unphases the portal for the Horde, but for the alliance you just need to complete the first 10 or so quests in the zone up until you collect muck from the water elementals.
1) Hearth to your faction's main city.
2) Take the Twilight Highlands portal to your faction's Twilight Highlands city.
3) Fly to the Alliance / Horde counterpart.
4) Take their portal!
For Horde this brings you within a minute of the Blackwing Descent raid instance. Access to central Kalimdor isn't too bad for the alliance, either. Unfortunately for alliance, you can't be mounted as you fly through... so you will be on the ground in Orgrimmar.
Screenshots of the portal locations:
Sorry, apparently the portal does not unphase for the Horde. This is alliance only!