I just returned from eight days in Turkey with my two kids 16 and 13. They are also frequent travellers and Turkey was the end of a 3.5 week trip to six countries.
Istanbul is great - we saw the Hagia Sophia, Blue Mosque and Tokapi Palace but our favourite was the underground Cistern. We also went up the Galata Tower and walked across the Galata Bridge (nice restaurants underneath). We liked the Spice Market better than the Grand Bazaar - not as big - but they were both neat. We spent three full days and could have done a fourth to get to more sites, but the heat and humidity in early August is tough. You'll do better in the fall. Use the Rick Steves book and try to stay in the Sultanahmet (we stayed at Grand Peninsula). The biggies are just a five minute walk and the local tram/streetcar is easy and cheap.
We spent two days/nights in Cappadocia and loved it - probably one of our favourites. If you can swallow the expense, go hot air ballooning at sunrise (110 Euros each). We stayed at the Flintstones Cave Hotel the second night, which is not as hokey as it seems, in fact very elegant, but the best thing - it has a beautiful pool. The kids convinced me to spend a morning just hanging in the pool and it was lovely - wonderful views as well. I rented a car at the Nevsehir airport and had zero issues driving around Cappadocia - signage is good and lots in English and the car also had a GPS. I don't drive a stick, but asked for the smallest possible automatic, as parking spots and many smaller roads are very narrow. We flew in and out of Cappadocia from Istanbul - rates are decent and worth the time as it would be a 12 drive one way.
We also flew to Izmir and stayed in Selcuk to see Ephesus (Bella Hotel, very nice rooftop terrace). Ephesus is great and worth the morning, but not a lot more to do in Selcuk other than the local castle for an hour. In retrospect, I would have just stayed one night and moved on (instead of two). If you are thinking of going down the coast, perhaps rent a car at the Izmir airport (also a 12 hour drive from Istanbul, so fly if you can), and then travel down the coast of Turkey.
Check out Turkish Airlines for the flights - it's now my favourite airline in the world! Super nice people, good rates, free checked bag and a very decent lunch for a 1 hour flight - you don't get that in North America!
Safety-wise - as a single mom travelling with two teenagers, I felt safe at all times - never a single issue. I did have one man ask where my father was or my husband was (!), but everyone was very kind, especially in the smaller towns. Lots of English speakers and even French. Ignore the vendors in Istanbul who hassle you with every step.