Answering my own question after taking the time to trudge through the temple.
It appears that no, there is nowhere to sit inside any of the first three temples, namely:
- Skyview Temple
- Earth Temple
- Lanaryu Mining Facility
However, there are stools just outside the entrance to these three, within close distance to the Bird Statue that corresponds to the entrance. This pattern seems intentional, considering the rarity of seating in regions such as Eldin Volcano and Lanaryu Desert.
- Skyview Temple: A small stump or cut log under the large tree west of the main entrance
- Earth Temple: A small decorative column juts out from the wall to the immediate right of the entrance, behind the Bird Statue.
- Lanaryu Mining Facility: A small stool is placed on a ruined wall just north of the entrance, east of the main power generator.
If anyone finds a seat inside that you can get to from the first encounter of these places, let me know. I'll try to update with interior locations upon revisiting for the later quests.