It is a 619 kilometer (385 miles) distance between Istanbul and Pamukkale, a drive of 8 hours. There are direct flights and busses available between Istanbul and Pamukkale, so you have many options to travel.
It will cost about €100,- ($115,-) for the two-way ticket with Turkish Airlines to Denizli Cardak Airport. The flight takes one hour.
From the airport of Denizli Cardak you can take the bus to the busstation of Denizli called Otogar Denizli. This will cost you about €20,- ($25,-). From the Denizli Otogar you can take the minibus described here above for about €4,- ($5,-). All the prices are in two way calculated. So in total it would be around €130,- ($150,-).
Bus companies don’t take you directly to Pamukkale, but to the Denizli otogar bus station. There are busses operating every day from Istanbul to Denizli. You can buy your tickets from the following bus operators: Pamukkale, Kamil Koc and Metro Turizm. Bus services include water, cold or hot drinks and snacks.
The bus drive from Istanbul to Denizli otogar bus station will take about 12 hours and costs 80 Turkish Lira (11 euros or $12,-) for one way.
The bus will drop you at Denizli otogar bus station and then you have to get on the minibus (Turkish: Dolmus) to Pamukkale. This is about 18 kilometers / 11 miles away. The minibuses depart the Otogar’s Platform (Gate) 76 on the lower level (below the intercity bus gates) every 15 to 20 minutes. For the minibus from Denizli otogar to Pamukkale the price will be 5 Turkish Lira (0,75 euros or $1).
It’s a 619 kilometer (385 miles) distance between Istanbul and Pamukkale. By car this will take a drive of 8 hours.