Biano Hills
This is the very first thing you do in the game. When you make the statue appear by the beach, Shadow Mario runs off with the Princess. He follows a set loop around town, so follow him and spray him whenever you can. Eventually he'll fall down - follow him to that statue and he'll put a colorful M on it and leap through. Spray it and you'll be able to follow him into this first world.

Ricco Harbor
After you earn 3 shines, you can now get into your second world: Ricco Harbor. A goo mess will appear on the docks. Go there and wash down the slime, then kill the plant that appears there. Now the Blue Coin Trading Shop will appear at that spot. You can trade in every 10 blue coins you get for a shine! On the side of a shop is a colorful M. Wash it and then hop into it to get to this world.

Gelato Beach
After you earn 5 shines, the lighthouse gets covered with goo. If you face the main beach, it's on your far left hand side by the pier posts. Go and wash away the slime and fight the plant that appears. After you destroy him, the lighthouse will rise up with a colorful M on its side. Jump through this to get to the Gelato Beach.

Pinna Park
After you earn 10 shines, the Princess is captured. She's taken to Pinna Island. You can now follow her by using the red cannon in the top left corner of the map, if you're standing on the beach with the water behind you and the town in front of you.

Sirena Beach
After you finish Episode 4 of Pinna Park, you'll return to the main area to a Yoshi Egg Chase. You end that episode by warping back to the center, and the game says "Go!" The Evil guy has the Yoshi egg. Water him enough so he drops the egg. Now you can get Yoshi by bringing him the fruit he's thinking of. The thought bubble will show a banana or pineapple or whatever. Note that Yoshi shoots out juice of the color of the most recent fruit you've eaten! Take him up on the roof and have him eat the giant pineapple there to jump into the pipe.

Noki Bay
After you get 20 shines, a rainbow shines down into the center of town. Stand in the rainbow and then look up into the sky - right at the sun! Yes, do NOT try this in the real world, it burns out your eyeballs. But in the game it gets you to the next level.

Pianta Village
Once you get the rocket nozzel (30 shines), go behind the giant shine in the center of town and rocket up to the top of it. There's a red tube up there that leads you to this area.

There's a different way to get to town. Go onto the smokestack of the boat with the gangplank. Jump+hover to the walkways. Jump down to the town. -- from The King of Videogamia

Super Mario Sunshine Walkthrough