After you gain the power to become a painting, there is a lot of exploring you can do in Hyrule before seeking the pendants.
Get the Pouch
If you go past your house, the blacksmith's wife will walk past, calling for Gulley. Go southwest to find the blacksmith's wife standing in front of some bushes. Go north and cut the bushes so you can go into the woods to the north. Go to the tree stump in the center and take the bag. It's a Pouch. The blacksmith's wife comes up and tells you to use the Pouch, because Gulley was planning to give it to you. The Pouch allows you to equip an item to X in addition to being able to equip items to Y.
Get a Heart Container
Go to the Blacksmith's house and Merge with the east wall. You can walk behind the house, pop out and go north to get a Piece of Heart.
Kakariko Silver Rupee
You can go into the Kakariko jail and merge with the wall to get into the cell and get the Silver Rupee.
If you go north of the Fortune Teller that is north of Kakariko, you encounter Irene, the witch. Her fortune said she was headed for disaster unless she took care of green. So, seeing you, she has decided that since you wear green, she should take care of you. She gives you the bell, which lets you call Irene any time. She can fly you to any of the weather vanes that you have visited. Nice!
Go into the Fortune Teller's shop north of Kakariko Village. The Fortune Teller will give you Hint Glasses. These allow you to see Hint Ghosts in certain locations. You can pay a Hint Ghost 1 Play Coin to receive a hint. If you go to the home screen and close your 3DS, it can earn Play Coins for every 100 steps you take.
Northwest Woods Piece of Heart
There is a piece of heart that you can see in the northwest woods. You can only get to it by merging with the wall north of that piece of heart.
Go to the Miner's House. His name is Rosso and he lives just east of the northwest woods. Talk to him in his house and he eventually gives you the Power Glove. It lets you pick up small rocks. If you go outside and pick up all the rocks, the Miner rewards you with the purple rupee in the chest in his house.
Go to the Witch's Hut. East of it, you find a Zora who can't get back to Zora's Domain because the bridge is out. But you can use your Merging ability to get there, so do that. Go to the northeast area and you will find the Shady Guy running out of the waterfall door. He rushes off and then you hear a shout from Zora's Domain that something is wrong with the queen. Apparently the Shady Guy stole the Smooth Gem that keeps the Zora Queen's power contained. If she doesn't get it back, she will keep getting bigger.
Go to Kakariko Village. You discover that the smooth stone is for sale by the merchant sitting outside on the blue rug. Buy the smooth stone for 200 rupees.
Go back to Zora's Domain and go up to the queen's pond. Agree to throw in the gem. The queen, Oren, goes back to normal. She gives you the Zora's Flippers. Now you can swim! Press A to dive, press B to swim more quickly.
Zora's Domain Piece of Heart
Using Zora's Flippers, get in the water south of Zora's Domain and go south down the waterfall. In the cave behind the waterfall, you find a piece of heart.
Rent Stuff from Ravio
When you go back to your house, you discover that Ravio has turned it into a rental shop. Ravio will let you rent things and keep them unless you fall in battle. His bird Sheerow will take the rental stuff if you fall in battle. Right now you can rent bombs, the Tornado Rod, the Hookshot, the Ice Rod, Fire Rod, Boomerang, and Hammer. You can rent more than one item at a time, so feel free to rent everything or just a few things.
Runaway Item Seller
In the area south of your house, there are two rocks on the left side. Put a bomb between those rocks to open a secret cave. You find the Runaway Item Seller. After listening to his sad (pathetic) story, he asks you to bring him a Scoot Fruit. You can buy one in the Kakariko Item Shop. He'll give you 100 Rupees for the Scoot Fruit.
South of your house and one screen east, you can get a purple rupee in a dark cave. Equip your lantern and use it on the torches to make a chest appear. It contains a purple rupee. Ropes fall from the ceiling when the chest appears, so watch out.
South Hyrule Piece of Heart
There's a hidden cave entrance between two large statues in the screen south and east from your house. Use a bomb there and go into the cave, then find the western exit from this cave to reach a Piece of Heart.
Letter in a Bottle
In the southeast area of Hyrule, you find a message in a bottle on some shallow water. Go get the bottle. The letter is from a mountain climber who fell and hurt himself. He's past the Tower of Hera and he wants some Premium Milk, which you can get at the Milk Bar in Kakariko Village if you show the owner the letter. He gives you the milk and asks you to take it to the customer. It's a difficult climb to reach him, but you get an empty bottle for your trouble.
Tower of Hera Piece of Heart
You can get a Piece of Heart by going to the Tower of Hera and going west to Spectacle Rock (the volcano). Merge with Spectacle Rock, then go to the south middle and pop out of the wall. You fall down to a cave entrance. Go north through it to get the Piece of Heart.
Kakariko Piece of Heart
After you get the Power Gloves, you can pick up the rocks in northwest Kakariko Village and drop into the well to get the Piece of Heart at the top.
Once you rent the Hookshot from Ravio, you can go to the north part of the northwest forest and use the Hookshot to reach the hollow log across the gap. The guy inside will tell you gossip about different people.
After stealing the Zora's stone, the Shady Guy is hanging around in Kakariko Village, just east of the weather vane. If you try to go up to him, he runs away. Merge with the wall northeast of the Shady Guy and then pop out right behind him. Instead of running away, he'll apologize for stealing the Zora's stone, then will give you the Pegasus Boots. Press L to dash.
If you get Zora's Flippers as described earlier on this page, you can swim under the bridge that is east of your house. Talk to the Bird Lover, say that you like birds, then choose "Let's Talk". He will give you an empty bottle that washed up on shore.
Continue your Quest
When you are done exploring, you should go to the House of Gales or the Tower of Hera. You can go to them in whichever order you prefer.