Please help a new Alliance player with a travel problem.

I recently picked up WOW again having not touched it since 2007, even then I didn't go very far. I apologize for the newb question, but everything online anymore seems to be geared toward the elite.

Anyway, I'm a level 22 Dranei mage who was summoned to Stormwind by the trainer there as part of the "Mastering the Arcane" quest.

That quest requires me to travel from Stormwind to Shadowfang Keep near the Silverpine forest. I can't find a way to do this even relatively safely.

I tried going through the Arathi Highlands and heading west from there, but there is a lot of sudden death that way for members of the Alliance.

I really want to give this another go tonight and would appreciate any help.

EDIT: Thanks, folks. I've done a dungeon before, which makes me feel really stupid for not thinking about that. I guess I expected more direction in-game.

EDIT 2: I got my Staff of the Royal Wizard! Hooray! Thanks again.