Leypoint at G-8 in Wajaom Woodlands
Note: After you receive the lightning band, the quest is over. The Olduum Ring, technically is in no way associated with the quest, Olduum.
Completion of the Olduum quest will grant a Lightning Band. This can be traded to the Leypoint for an Olduum Ring. Similar to the Outpost Warp function of devices such as Return Rings, this ring allows instant transportation to this Leypoint.
Also if you trade 500,000g to the NPC in Tenshodo Headquarters to get your Boarding Pass, he knocks you out and you wake up here.