I don't think you could fit Ankara in this 10 day trip.
Are you planning to spend any time in Istanbul? If this is your first trip, you'll want to spend at least 2-3 days there.
Now fly to Kayseri or Nevsehir, and then make your way to Urgup. Spend 2-3 nights there. I assume you're planning to take the hot air balloon ride and do some exploring? Instead of Urgup, we stayed Goreme, in the Kelebek Cave Hotel, and really enjoyed it. It has a lovely pool, which you will want this time of year. They offer an airport transfer for 10 euros per person from either Kayseri or Nevsehir.
Next, take a bus to Konya, and spend one night there. Fly from Konya to Izmir and spend one night.
That leaves 2-3 nights for the Seven Churches, and I think you'll need to find a tour or a private tour guide in order to see everything in this time frame. I found a tour, although I have not taken it and cannot vouch for it -- but it shows the general itinerary and what's possible. With research I'm sure you could find others. This one starts and ends in Izmir and includes an overnight in Pamukkale.
This would be a very ambitious trip but very interesting. Be prepared for extremely hot weather.