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Back in 2008 we stayed as a family in a terrific rented old monastery turned holiday residence in the small village of Lapta or Lapithos. It was out of Kyrenia ( aka Girne), but you could get there, traffic permitting in about 20-30 minutes. We went in October and it wasn't busy at all.We also found a superb family-run restaurant just up the hill from where we were staying.There were several beaches nearby but we did use the rented car to reach them. There are plenty of interesting places to visit as well particularly if you have a car to get around.I hope you manage to find somewhere suitable. We had a great time there. The day boat trip out of Kyrenia was the highlight.Regards,Mike