First off, I would suggest taking a look at the "Windurst" section of that. It lists several quests you can do for quick fame. Though the most effective one is what people would refer to as the cornette quest, AKA http://wiki.ffxiclopedia.org/wiki/Mandragora-Mad
It is suggested that you have a friend or a mule send you the Cornettes, as traveling between Windy and Bastok multiple times can be a pain. It takes 270-300 cornettes to max Windy reputation. With a friend, second character, or second account in Bastok you can go from level 1 reputation to level 9 in just under 2 hours.
So wait til Bastok is in First or Second in conquest and buy cornettes from the music store. Have your mule send them to your main in Windy and trade them one at a time to the quest starter. There's a chart on the Quick Reputation page that shows Cornettes to Fame, and how many you need per fame level.
Good luck. Edited, Aug 16th 2008 3:12am by Kalianaxx