I looked at the room photos on the Museum Hotel's web site and I think we were in the Guvercinlik room. In any event, it was very nice, not damp and had a big jacuzzi tub in the bathroom.
Definitely take the hot air balloon tour - it was fantastic and the highlight of the trip. There were at least a dozen companies launching balloons;your hotel can easily book that for you.
Our favorite stops were the Derinkuyu underground city (definitely go way down into it - there are at least eight stories open), the Goreme open air museum, meeting a woman who lives in one of the rock homes, champagne at sunset overlooking the Rose Valley, hiking through the Zelve valley and of course all the fabulous food.
here is a
link to our photos, which I have posted before.