There are busses from Nevsehir, Avanos and Urgup to Kayseri. Kayseri is a provincial center down the Erciyes-Mountain. At least a half day visit I strongly advise.
When you come to the central bus-station of Kayseri, take a service bus ( operated by the bus-company you use) to the city center. In the city center get off at "Duvenonu" the main square of the city. Easy to find since you easily find the big Hotel Hilton Kayseri. Start with a visit of Gevher Nesibe Medical School from the Selcuki Time. In the same area you find two nice examples of mosques from the selcuki time -Huant Hatun Mosque and Grand Mosque ( Ulu Camii or Cami-i Kebir). The basaar area is composed of some sections- main covered basar and the basar within the castle. A great experience.
Approximately 30 minutes by walking from the city center you find two interesting sites: The local museum where you find artifacts from the historical site of Kultepe, and The Armenain Church of Kayseri, which is still active. As for the last- named, because of the security concerns they do not seem to be very keen to let anybody inside if you do not have appointment in advance.
In Kayseri, you as a visitor should also taste the local specialities. Manti ( made of dough with onion, garlic and meat slices in it) and pastirma - a type of dried and spicy meat-containing food which I advise for breakfasts.
I suggest that Kayseri should not be neglected.