No, [Hestu][1] will not always end up in the [Lost Woods][2] (or more accurately, in [Korok Forest][3]). According to the [IGN wiki][4]:

> Hestu will finally make it to Korok Forest after you visit him at either Stable.

[This answer][5] summarizes Hestu's locations in great detail, though I will summarize them briefly below:

After initially meeting Hestu south of [Kakariko Village][6], and completing the [Priceless Maracas Quest][7], he will then move to a location south of Kakariko village (along the winding path) in west Necluda.

After 2 upgrades here, Hestu then moves to the left bank of the Hylia River, just northeast of [Riverside Stable][8]. Sometimes Hestu can also be found at the [Woodlands Stable][9]. And [some sources][1] suggest he can also sometimes be found at the [Wetlands Stable][11]. Nevertheless, more inventory upgrades are now available for purchase. 

Finally, Hestu will make it to [Korok Forest][3] where he will remain for the rest of the game.


  [1]: http://zelda.gamepedia.com/Hestu
  [2]: http://ca.ign.com/wikis/the-legend-of-zelda-breath-of-the-wild/Lost_Woods
  [3]: http://ca.ign.com/wikis/the-legend-of-zelda-breath-of-the-wild/Korok_Forest
  [4]: http://ca.ign.com/wikis/the-legend-of-zelda-breath-of-the-wild/Hestu
  [5]: https://gaming.stackexchange.com/a/302086/163757
  [6]: http://ca.ign.com/wikis/the-legend-of-zelda-breath-of-the-wild/Kakariko_Village
  [7]: http://ca.ign.com/wikis/the-legend-of-zelda-breath-of-the-wild/The_Priceless_Maracas
  [8]: http://ca.ign.com/wikis/the-legend-of-zelda-breath-of-the-wild/Riverside_Stable
  [9]: https://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwiKi66CjOPTAhUo4oMKHYsIBE8QFggpMAA&url=http%3A%2F%2Fca.ign.com%2Fwikis%2Fthe-legend-of-zelda-breath-of-the-wild%2FWoodland_Stable&usg=AFQjCNHD1JP6o0b0Y3PWFDENlLTluOHiEg
  [10]: http://
  [11]: https://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwid3O-djePTAhWL1IMKHScDAPAQFggmMAA&url=http%3A%2F%2Fca.ign.com%2Fwikis%2Fthe-legend-of-zelda-breath-of-the-wild%2FWetland_Stable&usg=AFQjCNGsuPCcn4NWq3lyPVJ_CTYg6cpBgw