I may be mistaken but i think, Devrek, Bartin, Ulus, Pinarbasi, Azdavay, Kastamonu, Kure. inebolu, Sinop, Samsun, Trabzon, Macka/Sumela, Uzun Gol, Rize, Ovid, Ispir, Bayburt, Gumushane, Tosya, Ilgaz, and back to Istanbul is a good route, bypassing Safranbolu.
You will find Erzurum, Bayburt and Gumushane rather backward with alcohol free city areas. i do not recommend that you do these parts solo.
If you prefer something different and start in Trabzon, flying there from istanbul, then you have the more lush vegetation above Hopa to Borcka, Macahel, Artvin, Savsat, then down to Yusufeli and Barhal. We found Barhal to be very popular with young Israelis. following the Kackars down towards Rize or West to Ispir. These areas have more hikers and you can find people you can join more easily, and I do recommend it. There is bear and wild boar as well as slippery and dangerous canyons and rocks.
Also check with Bukla tours for reasonably priced hiking-trekking-rafting tours. It is owned by some people from the area, who were very helpful to us giving us lodging and driving ideas and information which we could not have found anywhere else for no charge, two yeas ago.