In most parts of Turkey, dolmuses are practical. In Cappadocia, service is infrequent and at best unreliable following a circuitous hourly route from the Ürgüp bus station to Zelve, Avanos, Göreme, Üçhisar, and back.
Dolmuses also run to the smaller villages from select main towns, for example, from Ürgüp to Avanos or from Ürgüp to Mustafapasa (these generally run every other hour between 9am and 5pm). If you're headed further afield to say, Derinkuyu, you'll have to change in Nevsehir. A municipal bus provides service between Nevsehir and Avanos daily on the hour from 8am to 5pm.
Obviously, a day tour will solve the transportation problem.
Several car-rental agencies offering low daily rates of around 61TL per day are located in the center of Ürgüp, including Europcar, Istiklal Cad. 10 (tel. 0384/341-8855); and Decar, Istiklal Cad. 3 (tel. 0384/341-6760), while Avis has a location in Nevsehir at Istiklal Cad. Belediye Pasaji 10 (tel. 0384/341-2177). You may also save a few dollars by working with one of the neighboring locals. Scooters and beat-up old mountain bikes are also for rent in various shops along the market.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.