Saklikent is an amazing gorge that was recently discovered in the late 1970's. It is about a 30 minute drive inland to the gorge. The are unique restaurants where you can while away the hours feasting on 'gozleme' (special crepes made in this area) and fresh trout. It is also your staring point for an incredible 1-2 hour hike up the gorge. Make sure you are prepared with water shoes, bathing suit and a towel and change of clothes for when you are done. Don't bring a camera (it may get wet) and make sure you are physically fit to handle the slippery stones - and the cold water.
Hike in as far as you feel comfortable - it is loads of fun and what an adventure! The rock formations developed from hundreds of years of erosion have made the most beautiful shapes, the rock surfaces are so smooth, and the countless never-ending waterfalls are just awesome. One area in particular is stepped with perhaps six alternating waterfalls all made of smooth whites stone – it is a feast for the eyes. Other areas are in complete darkness and frightening until the gorge opens to the light again. It feel like your on an amusement park ride in Disney World – but it was so much better! On the way back down it is even more fun because you can slide down some of the waterfalls on smooth rocks into shallow pools of water. 
For those who are not comfortable hiking the gorge, you can stay at one of the restaurants inside the gorge. You can read, play cards, backgammon, paint, or take a nap. The proprietors will not bother you. You can stay for hours if need be. After the others return from their hike, you can lunch on fresh trout or gozleme and hear about their adventure.
TIP: At the place where they rent the plastic shoes you can ask for a guide. Do it! He knows all the ropes and can help the kids through the difficult passages. You can get much further into the gorge this way. You can tip him at the end - I usually tip $5 per person. The hike will take about 2 hours. You will be wet and the water is cold, so wear a bathing suite and a t shirt or long sleeve T shirt, Tevas or water shoes are a must, you need both hands free, and do not bring cameras or wallets, etc. They will get wet. Make sure you bring beach towels (the boat has some) and have them ready when you finish.