Cappadocia looks like nowhere else on earth. Millions of years ago, volcanoes around what is now Mount Erciyes buried this part of central Anatolia under thick layers of ash, which hardened into a soft rock called tuff. Wind and rain have been carving it ever since into valleys, cones and the tall, capped pillars that Turks call peribacası, "fairy chimneys". And because tuff is soft enough to dig with hand tools, people have been carving it too: houses, pigeon houses, wine cellars, whole cities underground and hundreds of churches, many of them painted from floor to ceiling between the 9th and 12th centuries, when this was a frontier province of the Byzantine Empire.
It's a region, not a city: a handful of small towns and villages, Göreme, Uçhisar, Ürgüp, Avanos and Ortahisar, a few kilometers apart in a landscape that changes color through the day. The rhythm here is early starts for the balloons and the light, long walks through the valleys in between, and slow dinners in cave restaurants. Five days lets you see the big sights, walk the best valleys and still have a spare morning or two in case the balloons don't fly.
This plan uses Göreme as a base. Day one is the balloons, the Göreme Open-Air Museum and the Rose and Red valleys, day two Uçhisar, the fairy chimneys of Paşabağ and Zelve and the potters of Avanos, day three an underground city, the old Greek village of Mustafapaşa and the wine town of Ürgüp, day four a trip to the Ihlara Valley, and day five Love Valley, Ortahisar and a ride at sunset. If you have longer, the best trips further out come after day five. The sites are open every day, so you can start on any day of the week. And when you're done, the rest of Turkey is a short flight away.