From the Lookout Landing, head southwest to the street. Go north at the first fork.
At the fork road where Yamiyo Shrine is located, go to the north. Don't forget to unlock it because it can be used a Travel Point.
Continue on the street and then pass through the Helmhead Bridge.
Continue walking straight ahead, and then you will finally see the Woodland Stable.
What To Do In Woodland Stable?
Unlock The Ekochiu Shrine
First of all, prioritize unlocking the Ekochiu Shrine, which is the nearest shrine to Woodland Stable. There is no need to rush completing the shrine, however it can be used as a Travel Point in order to return to Woodland Stable later.
The Side Adventure 'The Hunt For Bubbul Gems!' can be unlocked by talking to Kilton located at the balloon nearby. Give him the Bubbul Gem and he will give you a Bokoblin Mask that will be useful for farming Meat Food.
Tera Fountain is located northwest of Woodland Stable. Once you have received the request of 'Potential Princess Sightings!', you can start the Side Adventure of Great Fairy by talking to Penn at the Woodland Stable.
Enter the well near the Woodland Stable, then break the wall using a hammer or bomb flower, and you will find a hot spring in the back of the well. Getting in the hot spring will restore 0.5 Hearts at a time, so if you have lost a lot of Hearts, you can replenish it at the hot spring.