Well, that's wonderful to hear that you visited my country :)
Except Urfa, I have been to Diyarbakır, Mardin and Trabzon. For my photography and video profession :) Really nice places. Although Mardin and Diyarbakir were interesting in terms of history, Trabzon's nature was amazing. Especially the mountains and forests. I was also in Sinop for a short time, about 4 days. It was very enjoyable to watch the city and the Black Sea from Sinop Castle. It is also an incredibly slow city. The streets were very safe. I saw that there was no one inside the shops with open doors. In the past, it used to have a more provincial atmosphere, but recently it has become a place where young people are also popular and cultural events are organized for the last 10-15 years.
But I don't want to lie, Erzurum does not interest me at all. It doesn't seem to be a problem if I leave this life without seeing it :)
Maybe, you had seen a lot in Turkey, so Erzurum could add nothing to that. :)
I guess places to the west of this town are even quieter. Amasra is sort of famous there and Zolguldak has some industry (as I remember from some maps), the rest territory of that area is just "empty". I hope to find some Black Sea vibes there, vibes of the old times... I don't know. But it's not about today or tomorrow, I am in Southeast Asia (for 1.5 year) and have no plan to leave yet. :)