After you go into Stilled Goron City and repair the rift, you can explore Goron City.

Explore Goron City

In the lower level of Goron City, go through either door to enter the shop. There you can purchase potions, rocktatoes, and rock salt.

Go Outside

When you go back outside, there will be a cutscene. Your destinations will be marked on the map.

Go east and there is a treasure chest on a ledge. Open it to get 2 Might Crystals.

If you create a flying monster echo and pick it up, you can glide east and north to reach a Stamp Stand on a ledge.

If you went to the Stamp Stand, you can warp back to the entrance to Goron City. If not, you can stand on the air vent north of the chest to float back up.

If you go north onto the darker rock, you can defeat the rock monsters and learn the Tweelus echo.

West of that, there is a lava lake. There is a Fire Octo in the lava lake, but there is also one on solid ground to the east, across a flow of lava. Go east to that Fire Octo and defeat it, and learn the Fire Octo echo. Then go northeast and open the chest to get a golden egg.

If you use echoes to go up to the ledge above the treasure chest where you got the golden egg, you find a monster to defeat. If you can't find the echo after the monster is defeated, you can go into Goron City, then return to this location to find the echo floating in the middle of the lava pool. When you get there, learn the Fire Wizzrobe echo.

There is an island in the lava lake with a Piece of Heart on it. Before you try to get the Piece of Heart, go counter-clockwise around the lake to reach a lava rock on the ledge. Press ZR to learn the lava rock echo. Then you can create a lava rock in the lava lake (only one at a time because of the cost) to go to the Piece of Heart. Try creating a boulder next to the lava rock, but be aware that the boulder will sink into the lava after a moment. But you can jump onto the boulder and then create another lava rock to jump onto, and go through the lava that way.

When you're ready to move on, go to the southwest part of the large lava lake to find a waypoint. You can go north from there along the solid path to reach a cave. Go in to find the Lizalfos Burrow.

After you clear the Lizalfos Burrow, go west from the Goron City Smoothie Shop, then north up the slope, then east and up the slope, and use echoes to reach the Piece of Heart on the ledge. You may need to repair the Stilled Western Eldin Volcano rift to reach it.

Then go west from there to find a Stamp Stand in the lava.

Then go north from there and check on the waypoint. Then go north to enter the Rock-Roast Quarry.