In the Gnarled Root Dungeon, you receive Ember Seeds, which gives you access to the Eastern Suburbs. You can get there from Horon Village.
Items in Horon Village
Go back to Horon Village. In Mayor Ruul's house, you can bomb the wall to the right of the mayor. In the hidden room, there is a Gasha Seed.
There is a Piece of Heart in plain sight in Horon Village south of Mayor Ruul's house. You can get it now by burning the small tree in front of it with an ember seed.
In the southern part of Horon Village, there is a house with a fenced in area where you can see a treasure chest. First, go into the house and use an ember seed on the torch. You will receive the Cuccodex.
Use a bomb on the cracked wall in this house to reach the chest in the fenced area outside. It contains 20 rupees.
Go to the house with the girl surrounded by Cuccos and give her the Cuccodex. She lives to the east of the entrance to Gnarled Root Dungeon. The girl will give you a Lon Lon Egg. The next time you encounter Maple, she will take the Lon Lon Egg and give you a Ghastly Doll.
Go to the Eastern Suburbs
South of the Maku Tree, there is a sleeping guy and a kid playing fetch with his dog. When you approach the two small trees on the right side of this screen, the sleeping guy will wake up. He is Sokra, and he tells you to look for the Temple of Seasons, where the Season Spirits will surely help you.
Burn the small trees and exit to the east. You see a cave entrance here. It doesn't lead to any items right now, although you can see a Piece of Heart there that you can't reach, and you can meet Guru-Guru the windmill man, who needs oil for the windmill.
You can go south from here through a log to find a beach. At the end of the beach is a skeleton pirate guarding the gate to Samasa Desert. He can't leave unless he finds his captain's bell.
From where you first entered the Eastern Suburbs, go north, then east. A strange creature with a bow in her hair will rush past, saying that a temple fell into Subrosia, which is a secret place. She goes north, saying that she needs to go back to Subrosia without being seen.
You need to find that temple, so follow her north. She will wander around this area. Follow her without letting her see you. At one point she will exit the screen past a fence. Don't follow her right away, because she'll come back and look around one more time. Follow her after that. She'll disappear into the top-left bush. Cut that bush to find a portal to Subrosia.