First thing: IF you are planning to do the hot air balloon ride (it seems most people have that as their #1 Turkey bucket list item), then you really want to book that flight for your first morning in Cappadocia. Because the balloons only fly when the wind is calm, and often the wind is not calm. In that case you have the option to be rebooked on the subsequent days. If doing the balloon ride is important to you, plan this first, and build the rest of your itinerary around it, in order to give yourself the greatest possible chance of it happening. (FWIW, I thought the balloon ride was fun, and yes a bit of an expensive splurge, but what you gonna do when your spouse has been dreaming of it...).
Tips for (maybe) a better balloon experience:
- Shop around. Competition is fierce. Pay in cash for a discount (they prefer Euros).
- Some balloon operators have larger/smaller baskets (more/fewer passengers sharing the experience with you). Ask how many they will squeeze in.
- Try to be among the last to climb into the basket: the first people on tend to get pushed to the center (surrounded by other people), the last on tend to be on the outside, enjoying less-obstructed views. At least that was how it was for us.
The "sights" around Cappadocia are widely scattered. A car will be very handy, unless you want to pay for every excursion out to see/do anything. There are plenty of "tours" you can pay for, but if you prefer not to be part of an organized group, a car will be necessary. We rented a car at the airport in Kayseri (actually just outside the airport, the agency office was off-airport, they met us at the airport and drove us to the office for the paperwork). Driving around Cappadocia is easy.
About the "cave hotel" experience: we stayed in a nice one (used by RSE tours, I believe) and while it was OK, it was still...a cave. A little musty with with funky smells around the bathroom. It wasn't awful, but it wasn't completely awesome, either, and if I went back, I'd probably choose a more conventional hotel for more comfort.
Sending a PM with a link to more info. Cheers.