Diddy (& Kirsty)
That's an ingenious suggestion, but I don't think it's Nydie Mill.
"Neidy Hill" is shown on Ainslie's map of Fife dated 1775. It was in the parish of Ceres, just under 3 miles east-south-east of the village.
Later maps (from 1828 until today) show a farm at - or very near - this site, called Bankhead. Maybe they changed the name.