If you liked
Tsuki ga Kirei
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...then you might like
Itsudatte Bokura no Koi wa 10 cm Datta.
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Both shows are serious, melancholy, straight-forward romance stories with no fan service and characters who act like real kids. 10 Centimeters is a little more dramatic and a little less focused on the small details of life, but is generally in the same vein.