The best way to reach this sight would be renting a scooter or car. It is a steep ride uphill on a bicycle and takes a long time by bus (two hours each way). Take the main road east out of Parikia and then take a left a few kilometers out when you see the sign. It is all uphill from there. The road ends and turns into a dirt road. The drive is probably one of the best parts of this trip. There are majestic views of the unreal blue sea and the landscape is lined with ancient rock walls. High on the mountains you can see the sides spotted with blue-domed churches. You can also visit the nunnery Khristoú stoú Dhássous on the way, although only women are allowed into the building. Men can make it as far as the courtyard. Just follow the signs on your trip.
Peta-Loudhes is a park with millions of Jersey tiger moths hiding in the bushes and trees. There is a small fee to enter, but worth it for the shade and a quiet place to rest. It is thickly forested. The park is open June through September from 9AM to 8PM. The butterflies themselves are actually hard to find. They hide underneath the foilage and don't often make an appearance. I had a vision of thousands of them dancing around me and brushing softly against me, but unfortunately this is not the case. It is illegal to touch or disturb them so don't think you can create this scene yourself with a little shaking of a tree. But when they do take flight they are nice to see because the underside of the wings are a vivid red which contrasts with the blackness of the rest of them. There is a bathroom here and also a small place to get a drink and snack.
This trip is mainly worth it for the drive and the rest at the top of the hill. Don't expect much from the actual butterflies and you will be pleasantly surprised.