Pasabag Fairy Chimenys, also known as the Monk Valley, is easily reached without going for a tourl there are hourly buses from Goreme that will stop you near one of the junctions. We caught a bus over to Pasabag from town for about TL3, and got off just as most of the tour groups left. From the junction it's about a 20-30 minute walk to the fairy chimneys.
The walk is pleasant, especially with the shifting scenes. The scenery truly is amazing, one of those places where the terrain looks different from every angle. You can turn the corner and suddenly realize there's a gorge or another angle of the fairy chimneys, just lots of amazing surreal looking geographical formations.
Make sure you bring good hiking shoes, as parts of the trek to the fairy chimneys are sandy! You can actually walk through the valley, and see the panorama of the countryside, or trek further up above the fairy chimneys to see them from another angle. We didn't have time for the whole trek across, but we did see some people walking across the valley, and I dare say it would have been a nice hike across.
The buses on the way back seem more irregular than the buses there though, so we did have to wait awhile before managing to catch a bus, but we just sat down in front of one of the small shops by the road opposite the chimneys and passed the time.
For more photos, check out the hashtag #FoxyTravelsTurkey on Instagram.