Hyrule Field - Kakariko Gorge Piece of Heart Locations
There are 3 pieces of heart for you to find in Kakariko Gorge, the second part of Hyrule Field that you visit in the game. The first piece of heart can be acquired right after you lift the Twilight over the area. All it requires is the Gale Boomerang to reach it.
The second piece of heart can be acquired after you clear the Goron Mines and get the first Bomb Bag. Finally the last piece of heart you can find here, #<> can only be grabbed way later in the game once you have access to the Double Clawshot.
Kakariko Gorge - Heart Piece on the pillar
In the southeastern section of the Eldin Province of Hyrule Field in Kakariko Gorge you'll find a heart piece atop a lone stone outcropping. It's not very hard at all to spot and grabbing it with the Gale Boomerang is easy as pie. If you're having trouble figuring out where this is just use my screen shot below.
Additionally you can also find the Golden Pill Bugs nearby which you can scoop up when you grab this Piece of Heart. If you're far enough ahead in the game to where you have the Shadow Crystal and can collect Poes, there is one of them nearby as well.
Kakariko Gorge - Heart Piece in the Cave
Once you acquire a Bomb Bag early on in the game you'll be able to get this piece of heart from a cave in the southern part of Kakariko Gorge. There's an obviously destructible boulder in the southern portion of the gorge on the side closest to Kakariko Village, as seen in my screen shot above.
Destroy the boulder to open up a cave which you can enter. It's rather dark inside but you'll want to save your lantern's oil and not use it for light but rather use it to burn down the spider webs which block your path. Additionally you'll need the lantern to light the torches you come across.
If you're extremely short on lantern fluid you only actually need to light two of the torches - the two you see in the screen shot below. They'll make the chest appear which contains the Piece of Heart we're after. In the room just next to the Piece of Heart you'll find one of the Poes that you need to collect.
Kakariko Gorge - Double Clawshot Piece of Heart
The final piece of heart you're able to obtain in the game outside of a dungeon is this one. Since it requires the final dungeon item, the Double Clawshot, to reach. This piece of heart is found in the same place in Kakariko Gorge as the first one - the same pillar you found the first piece of heart on has a Clawshot location on it which we can now make more use out of since we have the Double Clawshot.
As you could have probably already guessed, Clawshot out to the location you see before you and once you do you'll notice another Clawshot location on the side of the cliff we just came from. Clawshot to that one then back to the vines which are hanging off one of the pillars in the gorge.
Circle around those vines and you'll find the chest which holds the final over world piece of heart.