As an Alliance player in Classic, you dreaded this run every time...

Straight across the water. There's just some murlocs on the way, and in case you were a druid you could use forms for quicker transport both in water and on land :) I wasn't a druid though :S I just blinked whenever it was off cooldown.

Reminds me of the epic journey to learn 2-handed swords if you were a night-elf. Had to take the boat from Darkshore to Menethil Harbor, run through Wetlands, while aggroing all the ?? skull crocolisks, running through Loch Modan, Dun Morogh, and then finally reaching Ironforge so you could take the tram to Stormwind to talk too Woo Ping, the most inconvenient weapons master ever.