For a story set in a small town, 'Willow Creek School' would be a nice name. It has a rural and cozy feel. If the school in your story is supposed to be very old - fashioned, 'Elderwood Academy' with its connotations of old trees and tradition could work well. Another idea is to use names related to the school's specialty. For example, if it's a school for future scientists, 'Nova Science Institute' would be appropriate.
Greenwood High School. It gives an impression of a school surrounded by lush greenery, which can be a great setting for various stories like a mystery involving the woods near the school.
Silvercrest Boarding School. The word 'Silver' can suggest something precious and elite, while 'crest' gives a sense of pride and heritage, making it a great name for a boarding school in a story.
Starlight Boarding School. The name 'Starlight' gives a sense of magic and wonder. It can imply that the school is a place where students can shine like stars and reach for the sky, with a touch of the extraordinary.
Sunnydale High School. It gives a sense of a place full of sunshine and positive energy, which can be a great setting for various stories, like tales of friendship and growth.
Sunrise High School. It gives the feeling of new beginnings and hope, which can be great for a story setting. Maybe the story could be about students starting their journey at this school and facing different challenges and growth.
Phoenix High School. The phoenix is a symbol of rebirth and transformation. In the story, the high school could have faced some kind of disaster or setback in the past and is now rising again. The students could be part of this renewal process, either by rebuilding the school's reputation or by changing themselves for the better.