After you find a Star Piece on the mysterious Star Hill, you can move on to Seaside Town.

Explore Seaside Town

In Seaside Town, the townspeople don't seem to be feeling so well. If you explore, you will find a shop, as well as an inn where you can stay for free. This shop will disappear when you get the next star, so be sure to buy what you want from that shop before then! Each item deals damage to enemies. Bad Mushrooms and Fright Bombs only affect one enemy (contrary to what the Fright Bomb description says), while Fire Bombs and Ice Bombs damage all enemies.

Go into the northernmost house in Seaside Town and talk to the Elder, who asks you to retrieve the Star Piece for him. Upstairs, you can talk to the Frog to purchase items with Frog Coins. They're pretty expensive, so you might want to come back later.

After you talk to the Elder, you can exit Seaside Town, and you will be able to go west to the Sea.