Natasha - there is plenty to do if you stay in Cappadocia for 3 nights (which is actually just 2 full days). We did our trip in the opposite direction from yours, flying from Istanbul to Kayseri, where a shuttle from our hotel (the Kelebek) met us and brought us to Goreme. It was a great hotel with a pool and spectacular views of the fairy chimneys in Goreme. We arranged our hot air balloon flight through them, with Butterfly Balloons. After the balloon flight they took us to a nearby farm for an “organic breakfast”. We spent the rest of that day at the Open Air Museum, with more than 30 churches carved from the soft rock. The next day we took a tour through the surrounding area, again arranged through the hotel.
Then we flew to Antalya but did not stay there. We left immediately on a bus to Patara, a tiny seaside town with an amazing beach, some great ruins and one of our all time favorite hotels, Akay Pension. Not luxurious like the Kelebek, but this basic little (very inexpensive) hotel had the kindest owner we ever met. They cooked a meal every night for hotel guests; at breakfast they’d tell you the menu & ask if you wanted to eat with them. It was absolutely the best food we had in Turkey. From Patara we made day trips to Saklikent Gorge and the sunken city of Kekova. We did not have a car — used the frequent buses.
From Patara we went north to Dalyan, a lovely little touristy town — lots of Brits here. Our hotel, the Kilim, was lovely and had a private dock out back with great views of the Lycian tombs carved into the cliffs across the river. We took a fun river cruise one day ending at the mud baths. At Itzuzu beach in Dalyan they have a sea turtle hospital which we found fascinating.
From Dalyan we went to Datca, another pretty little town. Our goal here was to see the ruins at Knidos. From Datca we took a bus to Marmaris and then a ferry to Rhodes, Greece. I think if you could drive from Ephesus down the coast, as David plans, rather than flying to Antalya, you would really enjoy visiting these little places along the way. We were there in early September 2013 and saw no crowds anywhere.