It's been a long time since I played. When I last played, Dalaran had portals to all the original cities, but they are gone now. Is there a new city with portals?
The Mists of Pandaria capital shrines in the Vale of Eternal Blossoms in Pandaria have portals to all major cities, plus Dalaran and Shattrath. You can ask a mage for a portal to these shrines. Please note that extremely low level players might get attacked by high level birds.
In addition, the faction base on the Ashran island has portals to 3 major cities: Orgrimmar, Thunder Bluff and Undercity for Horde, and Stormwind, Ironforge and (I think) Darnassus on Alliance side.