My family will be in Türkiye the first two weeks of April. Very much looking forward to the trip. It will be the 25th country for our two world-seasoned daughters.
The first few days are in Istanbul. We have a friend there who will be hanging with us and showing us around part of the time, so we’re fully squared away in terms of highlights, recommended activities, and so on. The last few days are in Izmir, and we’re set there as well (including a day trip to Ephesus).
In the middle, we’ve got time in Cappadocia.
We will have three full days, not counting the bookend days for traveling. I’m hoping for some specific recommendations for and against activity options, based on actual experience.
We’re staying in a cave hotel in Göreme, so that bucket-list item is ticked. We have a car rented, so we’re entirely flexible about where we go and when; we’re not dependent on tour operators or taxi services.
We’ve only pre-booked two activities: 1, a balloon ride for our first morning (so if weather doesn’t cooperate, we’ll have two more days where we can reschedule), and 2, a culinary session where we shop in a local market and then go to someone’s house to help make dinner and learn about the food.
The rest of the time, we’ll be hiking, looking at archeological sites, and so on. That’s the subject of this thread: soliciting input from anyone who’s been there and can speak to the pluses and minuses of various experiences.
Like, for example, we want to visit one of the famous underground cities, but probably not more than one. So, how do we choose between Kaymaklı versus Derinkuyu? Or another, if there’s an underrated alternative?
How do the various valleys compare? The organized tours all seem to visit Pigeon Valley, many go to Love Valley, there’s also Paşabağ (the Valley of the Monks), Rose Valley and Red Valley, and more. If we visit, say, two, or maybe three, which are really worth seeing? Which will be busy with tourists and which will be quieter and more out of the way?
Other sites? Uchisar Castle, Selime Monastery, the Goreme Open-Air Museum, etc.? We’re trying to prioritize because we don’t want the cave buildings to start to blur into one another. 
The town of Avanos? It looks lovely in pictures, they’ve got pottery workshops, and the underground art museum seems very nice. Yes, no?
Any other thoughts, comments, suggestions would be very much appreciated.