Karpathos' highest point is Mount Kali Limni. The highest point is 1215 meters and from the top, you'll have an amazing view from where you'll be able to see both ends of the island!
The hike is a bit challenging, especially the higher you get, but still doable for anyone with a normal level of fitness.
You can park your car at this Kali Limni taverna and from here you'll start hiking. The climb up is around 1,5 hours and back you'll be a little faster than that since you're going down which is easier for most people.
Good to know
Of course, you don't want it to be too hot but you don't want it to be cloudy either. When it's cloudy you will miss the beautiful views. Try to pick a good day :) Also, don't forget to bring water and a snack while hiking!