From StrategyWiki, the free strategy guide and walkthrough wiki

Blue coins are not simply coins that are blue; for every ten that you collect, a Shine Sprite is waiting as your reward. There are many blue coins spread out around the game; you'll find them inside zones and out in the streets of Delfino. There are 240 blue coins to be found throughout the game.

Take your hard earned collection to the bear in the boathouse (the portal to Ricco Harbor) to buy Shines with them. You'll need 10 Blue Coins for a single Shine.

Head to one of the following pages for more information on how many blue coins there are in that area and how to acquire them.

• Delfino Plaza

[edit] Graffiti X's (x2)

There's a pair of X's in the south part of Delfino Plaza: one is on the side of the statue in Bianco Sqaure, the other is round the back of the bell tower building to the west of Bianco Square. You may want to use the Turbo Nozzle to get between to two locations quickly enough.

[edit] In jail

If you look into the jail house on the east side of Bianco Square, you can see a blue coin in there. To get it, go round the back of the jail house (in the water) and you'll see a hole in the wall just above the water level. Get close to the hole, then jump out the water and use the hover nozzle to gain a bit of extra height - this will be enough to get you into the jail house.