Yoake Mae Yori Ruriiro na Portable

The story is set in very distant future, in a time when mankind is just recovering from decades of war fought between Earth and a terraformed Moon. The war was so devastating that it set technological progress back by decades if not centuries, which is why the settings don't look futuristic. Although the world is now at peace, there continues to be distrust between the Sphere Kingdom (Moon) and the Earth Federation. Travel between the two is restricted for diplomatic purposes and confined to a single spaceport on Earth. So anyway, one day the lunar princess, Feena fam Earthlight, comes to the protagonist's house for home stay.