After defeating Master Belch, you can go to Your Sanctuary at Milky Well.
Milky Well Location
After you defeat Belch, go through the cave that Belch was blocking. You will reach a part of Saturn Valley that you could not access before.
Clean Up and have Coffee
Sit in the hot springs near where you entered Saturn Valley after defeating Belch.
Talk to the Mr. Saturn next to the coffee table, and say yes when he asks if you will drink the coffee.
Then go down the ladder, go west and go into the cave there. Talk to the Mr. Saturn on the left to receive some gifts. If you don't have room, go up the ladder to the shop and sell some things, or use the phone to drop things off with Escargo Express. You won't need the Jar of Fly Honey anymore, for example.
Optional: Go into the Northeast Cave
Heal up in the hotel. You can go into the cave northeast of the hot springs if you wish, or you can skip it and come back later when you are stronger. If you want to skip it, go to the last paragraph.
If you do decide to enter the northeast cave, the Photo Man will take your picture when you walk north of the coffee table.
The monsters in this cave can poison you and mushroomize you, so you might have to go back to Saturn Valley. Just sit in the hot springs to cure your status ailments, including mushroomization and unconsciousness.
Go east through the cave. When you are outside, go south. There is usually a Magic Butterfly in this area. Then go east into the next cave. Open the gift box to get a Coin of Slumber, then go southeast to find the boss of the cave.
Kill the Tough Mobile Sprouts first, then focus your attacks on Trillionage Sprout. These enemies are vulnerable to Fire. After you defeat Trillionage Sprout, go through the door and approach Milky Well to get the Sound Stone melody.
Exit Saturn Valley the way you first entered, go south through the Grapefruit Falls area to reach the graveyard tunnel, and go through it to reach Threed. From there, you can take the bus that goes to Fourside via the Dusty Dunes Desert.