Where does Hestu go after the first encounter?

After Hestu leaves the location where you meet him, look for Hestu near the Riverside Stable north of Batrea Lake.

After you expand your inventory, Hestu tells you he needs to go home to his Grandpa in Korok Forest. If you talk to him again afterward, you can ask him how to get there:

On the way, he stops near Riverside Stable along the Hylia river. After you upgrade your inventory a few more times, he continues his journey.

Eventually, Hestu will make it to Korok Forest. To get there, follow the Hylia River north.

According to this wiki, he can be found again at Wetland Stable due to getting lost on the way to Korok Forest.

Hestu will only allow Link to upgrade a few times before announcing that he needs to get back to Korok Forest. However, he gets lost on the way, and is next found at Wetland Stable, in the westernmost part of Lanayru. He allows Link to get several more upgrades before remembering the way back to Korok Forest and leaving again.

Additional information is found on the "wiki". I'm unsure if thats the official zelda wiki.