Zelda's Secret Well can be found in Hateno Village, behind the house that Zelda used there.
Well Location
You can find Zelda's Secret Well in Hateno Village by going south along the wooden walkway next to East Wind (the General Goods store) and crossing the bridge over Firly Pond. The well is located at 3302, -2298, 0130.
About the Well
The well contains a pool of water with some Hot-Footed Frogs. There is a chest that contains a Well-Worn Hair Band. There are two Brightbloom Seeds on the desk, as well as Zelda's diary. You can read the diary to start the quest A New Champion's Tunic.