The newly opened Nayuta no Kiseki official site may be lacking in gameplay details, but it does have lots of story and character info. Here's a summary.
Nayuta no Kiseki begins on Nokosare Shima (literally "Left Behind Island"). The island is located near the center of the Sciencia Sea, a vast ocean that is filled with countless islands.
Nokosare Shima and its immediate surroundings experience a strange phenomenon. Shooting stars and "ruins" are continually falling from the sky. This has gone on for a long time, leaving the debris piled up on the island.
Stones known as "Star Fragments" have been discovered in the areas where the space debris landed. By shining light in a certain way on the fragments, people can see the beautiful phantom world of "Lost Heaven."
The image of Lost Heaven shown in the Star Fragment features dynamic natural landscapes and beautiful creatures. People long for such a world, and thus gave it the Lost Heaven name.
Nayuta Herschel (CV: Kaori Mizuhashi)
The game's main character, 15-year-old Nayuta was born on Nokosare Shima and attends a school in the harbor town of Sanzerize, which faces the Sciencia Sea.
Nayuta's interests including observing outer space using the telescope and sextant his father left him. He has a strong curiosity about the unknown and wants to know why ruins are falling on the island.
The prologue listed at the official site is written by Nayuta himself. Nayuta seems to be expressing doubt about the common belief that the world is flat and has an end. The vision of Lost Heaven in the Star Fragments convinces him that the world extends even further than is believed.
Signa Alhazen (CV: Kenichi Suzumura)
Nayuta's 18-year-old friend since childhood. He's a member of a protection force in Sanzerize. He's so skilled with a sword, skills which he learned from his teacher Olvas, that he can take out the beasts that appear on the island all by himself.
Signa and Nayuta formed a business some years back. The business helps the people of the town.
Noi (CV: Ai Kayano)
Nayuta meets this small girl, who looks a bit like a fairy one might find in a fairy tale, somewhere along his adventure. She had a mysterious device called a Master Gear, but it was stolen by a man who suddenly appeared before her.