For the ginger-lime syrup:
Scrub and rinse ginger and cut into 1/4-inchrounds. Use a vegetable peeler to remove zest from limes.
Combine sugar and water in a small or medium saucepan. Cook until sugar dissolves, stirring occasionally.
Add ginger and lime zest. Bring to a simmer then remove from heat. Set aside for 1 hour.
Strain syrup into a container. Discard ginger and lime zest.
Store syrup in a sealed container in the refrigerator for up to 3 months.
For the fruit salad:
Place blueberries, melon, and peaches in a large bowl. Pour 1/3 cup ginger-lime syrup over fruit. Toss gently to combine.
Taste and add more syrup if desired.