This Adamantite Ore farming guide will show you the routes that I use for farming Adamantite Ore. There were no major changes to ores at Outland, so this guide can be used for Burning Crusade Classic (TBC) and Retail WoW.
Khorium Veins are a rare spawn of Adamantite Deposits, much like Truesilver is a rare spawn of Mithril, so sometimes you will find a few Khorium too.
Nagrand is one of the best places to farm Adamantite Ore because of all the caves (marked with red circles). The mobs in the caves are easy to kill and the caves are not that big, so it's usually worth going inside.
Netherstorm is also an excellent place to farm Adamantite Ore. Just like in Nagrand, I marked the caves with red circles on the map. But, you should only go inside if you have stealth or if there is a lot of other people farming in the zone. These are much bigger than the Nagrand caves, and the mobs are a lot higher level. (maybe with good gear it's worth clearing them)
Shadowmoon Valley is also a great place to farm. There are two caves in the zone, but it's not worth going inside them. It takes too long to get to the nodes, and you can farm more ores just doing laps in the zone instead.