We took a taxi from Goreme back to the airport in Kayseri then flew to Izmir on Turkish Airlines, an airline that serves delicious meals even on short in-country flights. The only downside is you've barely time to eat when they're back to collect trays.
We picked up a rental car in Izmir to drive to the coastal town of Cesme where we'd have lunch. I did the driving. The only challenge with driving in Turkey was figuring how to pay at the automated and un-personed toll booths on the highway.
After lunch we drove to the nearby town of Alaçati where we'd hotel reservations. But we couldn't find the hotel, this being a time before the ubiquitous mobiles with map software, so we stopped in a cafe. One of the young fellows in the cafe offered to escort us to the Hotel Incirliev by having us follow him as he drove to the hotel on his motorbike.