Star Island is quite small and, like other islands, gets its name from the way it looks from above. It offers only a few activities for you.
Sea Platform
Sail to the single Sea Platform and climb its ladder. A chest atop the Sea Platform contains a minor reward.
Blue ChuChu
Defeat the Blue ChuChu underneath the large southwest boulder for a Blue Chu Jelly. (Bomb the large boulder to expose the Blue ChuChu.)
Silver Rupee (via Treasure Chart #7)
Finding and opening Treasure Chart #7 (found at Windfall Island [D2]) allows you to pull a chest containing a Silver Rupee up from the Great Sea near Star Island.
Piece of Heart #27 (via Secret Cave)
Bomb the large boulder on the island’s west side to reveal a hole leading to a Secret Cave. Defeat all enemies here to reveal a chest containing Piece of Heart #27.