Hey Mike - I'll definitely leave Istanbul until the end, I love the idea of finishing there. The thing that attracted me to Eskisehir was what I read on LonelyPlanet: "Eskisehir may well be Turkey's happiest city". Also, I've read the night life is pretty good there, sounds like it's worth paying a visit.
Look up Maksim Müzıkhol & Restaurant in Eskişehir. It was across the street from our hotel (Soyiç Otel) and was extremely busy (and loud) on Saturday night. I wanted to go but the previous few days had been quite busy, the city was a madhouse when we arrived late on a Saturday afternoon and after a great dinner at the hotel and some backgammon I was too tired to join the party. While I haven't heard of the "happiest city" think and my time there was short (we left Sunday afternoon after a nice long walk along the river) the people I interacted with did seem high on the happiness scale. While significantly smaller (population c. 100,000) my personal nomination for "happiest city" in Turkey is Amasya. Night life in Amasya is rather low-key but it's enjoyable. I also recall some long conversations with a Turk at a hotel in Bodrum who was a native of Eskişehir. He was amazed that an American tourist even knew of the city--much less had spent any time there--and was definitely very high on the "happy" scale.
Kayseri I just plan to use as a transit city to get to Nemrut;
Nemrüt Dağı is the sort of place about which you can say, "You can't get there from here." The only direct ways to the general location are from the south (from Urfa) and the east (from Diyarbakır) and both involve a ferry that runs infrequently. Otherwise you go far out of the way and nearly in a circle to get there ;) Even then you still have to get to the site itself which is kilometers away from (not to mention hundreds of meters above) the closest public transportation stop. Given that sunrise and/or sunset visits are considered by far the most desirable and the steep narrow road the last few km even hiking there from the closest accommodation (Nemrüt Kervanseray) is impractical and dangerous.
This is why I made that odd-sounding suggestion to fly to Malatya from Ankara, take a commercial tour and then bus your way back to Cappadocia which may not even involve getting off the bus in Kayseri. Here's my suggestion for a commercial tour from Malatya People who have used and report here say mainly good things while others who have gotten there on their own without private transportation frequently report difficulties and/or being given bad information by locals who severely overcharge. The drive from Cappadocia to Nemrüt is a real candidate for "most boring and unattractive" I've experienced in Turkey--one way is more than enough... The only good part is when you take the old (shorter but much slower) way in after Malatya. I suspect that the tour I suggested will take that way at least once as other area attractions are along that route. The major bus route into Kahta definitely avoids it. I saw promotional prices in the neighborhood of 80 Turkish lira for that flight and even though it arrived at about 01:00 I can nearly guarantee that Guneş will provide an airport transfer for either free or a modest fee.
and the Black Sea coast attracted me as I read there are far less tourists on this coast than the south-eastern coast, and Rize looks beautiful in photos!
Certainly far less tourists (in most places) along the Black Sea but neither is it anything like the Mediterranean and Aegean coasts in the southwest. I've only spent about a week in total directly on the Black Sea coast (three different visits) and only during the autumn (September/October). While it has a certain attractiveness the weather tends to be cool, foggy/misty and dreary much of the time--the farther east (say beyond Samsun) the more this seems to be true. It is by far the wettest part of Turkey and only only region where rain/overcast conditions are common any time of the year. The sea might be warm enough for swimming in June--I know by September/October it is too cool and /or rough for many and for reasonable safety. There is very little in the way of coastal recreation (certainly no notable seaside accommodation) between and including Ünye and Rize. The Black Sea is supposedly named in part because of the predominate coastline--enormous basalt boulders that look black when wet. I'm not saying that it's bad but am saying that any vision of basking in the sun on a nice beach with a reasonably warm sea dos not have a great chance of realization during a short visit to the eastern Black Sea coast
It's good to know that the buses are of a decent standard as that's the mode of transport I'll be using most often I imagine. I'll also definitely consider adjusting my route to visit Aphrodisias, Pergamum and/or Ephesus as I'd like to see at least some Ancient Greek ruins.
I'd also love to visit Mardin, I'm just not sure I'd feel safe so close to the Syrian border at the moment. But maybe the situation will change by the time I come to Turkey. Fingers crossed.
Regardless of the situation in the southeast of Turkey and despite a reasonable time to spend (3 weeks not counting Istanbul) you risk turning a nicely paced itinerary into a forced march if you venture too far east or too far south beyond the places mentioned. Mardin does earn my fascination for being the only place I've visited in the world where truly antique (1,000+ year-old) and beautiful buildings are still in wide use for both residence and commerce. The old heart of the city is rather like Marrakesh where everything is still moved and delivered by human power. If you do decide to visit there I would suggest working your way there by bus to fly to Istanbul and omit the Greco/Roman cities in the central Aegean area.