It's funny how they don't mention the Potwatch NPC in Ul'dah having Orange Juice. I mean, if you're starting there ANYWAY...
There are a lot more NPC's that sell orange juice, you are right. We just wanted to post the nearest possible vendor in. Though, you have a point it may be easier to just teleport back to Ul'dah and ride a chocobo back to Vesper bay... Will try this out when beta comes back up! Thanks for the feedback
The absolute quickest way to do the dye quest if you don't want to go out of your way (for the Ul'dah people at least) is to go through the main quest line. One of the quests that has you go back to Waking Sands will reward you with 10 Orange Juice. After that, it's just hopping outside and talking to the quest NPC before you leave the area. The coincidence of the reward and the request makes me feel that the juice request is specifically because of this quest reward.
But for those who aren't at that point yet, yes, Ul'dah's the quickest option based on the starting point in the guide. I mention the above, however, because there is no guarantee that the vendor stock won't change from Phase 3 -> Phase 4. Edited, Jul 3rd 2013 12:04am by Ravashack