Choosing to bypass Istanbul and instead spend the majority of our Turkish holiday on the coast where the Aegean Sea meets the Mediterranean was one of the smartest decisions I've ever made. You can really run through all the important sites in Istanbul in a day if you're properly motivated. Take some pictures of the Hagia Sofia, the Blue Mosque, the Grand Bazaar, Topkapi Palace, and maybe of a whirling dervish or two, but then get out of the city.
The area around Fethiye and Oludeniz looks like Greece, but way less touristy and cheaper. In fact you can get to Greece under an hour on a hydrafoil. The deep blue waters are amazing and ancient ruins are around every corner. The best $20 I ever spent on a holiday was when we booked this day cruise around the area. They picked us up in the morning from where we were staying and dropped us off again in the evening. They also fed us an amazing traditional lunch that I still dream about. Twenty dollars are just a few hours allowed me to see all of this!