Tarrey Town is a new village introduced in Tears of the Kingdom that was currently under construction during the time of Breath of the Wild. It can be found on the eastern side of the Akala region of Hyrule. This town is the only place you can go to find Monster Extract so you will eventually need to visit this town if you are looking to complete the Teaching me a lesson side quests.
Even if you do not have this region or the tower discovered, finding Tarry Town is quite easy due to some of the very unique aspects of the landscape in this area of the game. Apart from death mountain which takes up a substantial part of this region, there is a very unique spiral style path on the eastern coast. This is very close to Tarry town and will help you find it fairly fast.
This map is quite zoomed out so you can get a real clear picture of where to find Tarrey Town in the akkala region of Tears of the Kingdom. Southeast from death mountain. North of the Zoras domain or along the eastern cost of Hyrule just west of the unique spiral path in the sea. Whichever way you decide to go about getting here, it is one of the easier ones to get directions to.
