Adamantium Farming Location
In order to farm in this location you will first need at least 215 Gathering Skill. This location is by far the best location for you to find Platinum, Adamantium and Garnet. In about an hour you can pull out 500-600 Adamantium Ore along with 100-200 Platinum and 10-20 Garnet, depending on fails.
I can't say I've found a better place to get Adamantium Ore then right here. If you're not going to use the Adamantium Ore it will also net you a pretty penny on the AH since Armorsmiths will need quite a bit of it. Below is a list of items you can find here:
Adamantium Ore
High-Grade Adamantium Ore
Pure Adamantium Ore
Platinum Ore
Garnet Ore
Big Garnet Ore
Below is a video I use of the path that works best for me. You can mine in any order you'd like, I still recommend watching the video however to learn all of the Ore spawn locations.
NOTE: If you're just gathering here for money you'll also want to gather the Hasia which is used in the Alchemy Profession to create potions. Hasia and Fresh Hasia sell quite well on the AH.
Adamantium Ore Farming in Beluslan
This area is another great place for you to farm Adamantium and Platinum Ore. The only downside of this area is that many other people are here since all the mobs around the fortress are neutral. Usually everyone that around the Fortress is a bot as well competiting for your nodes.
This area will be good after the bot pandemic that currently threatens Aion is gone. Also if you're not fully looking for just Adamantium you can also find Hasia over in this area.
Farming Adamantium In Upper Abyss
Usually I wouldn't recommend Extracting Materials in The Upper Abyss since it is a gankfest. However, this area is out of the way and very good for Platinum, Adamantium and Garnet. On each of these islands you will find 5-6 Adamantium Deposits at any given time. You will also find 3-4 Platinum Deposits. Usually there is only 1 or 2 Garnet per island if you're lucky.
The only mobs that are on these two islands are Wriggots, they are roughly level 32 and don't pose much of a threat. If you run out of Adamantium and Platinum Deposits on these islands head just a tad west to the main island and Extract some goodies there.