If you have visited Cappadocia in the rainy season, do not worry. There are still a lot of things to do. The first thing that you can do and probably the best will be visiting Kaymakli or Derinkuyu Underground Cities. As these are under the ground, it is actually the best time to visit these places.
You can go to Avanos for the pottery demonstration. Avanos is home to pottery art for over 4000 years since the Hittites and there are many places offering free demonstration with a possibility of trying how to make a pot as well.
Another nice option will be going to one of the local wineries and taste some beautiful wine of the region. There are 2 big wineries in Cappadocia: Kocabag Winery and Turasan Winery. Kocabag winery is located in Uchisar and it is about 5 km away from Goreme. Turasan is a bit more further than Goreme about 12 km and it is located in Urgup town.
The final option will be visiting one of the rug cooperatives that you can learn all the process of producing a hand-made carpet.