Balei grew up in Poni Island in Alola, she stayed there up until she got her scar and then she moved to Malie City, this is where she lived for the rest of her life!

Back to Poni Island she lived a pretty chill life in the Seafolk Village save for the trainer pokemon incident, she spent a lot of her youth climbing and exploring around the Vast Poni Canyon. Living in a town of boat houses made her appreciate the waters as well, sometimes she would go diving and collect shells!
TL;DR: She had a fun childhood full of adventure