@Jerara
I intend to reside in Türkiye in roughly 1.5 years so I'll share my findings from my research in selecting my target city to settle into. Here are my comments to address your questions:
Safety/crime - My family and I have travelled throughout mostly the western half of Türkiye on road trips and never have we experienced any sense of danger. One time, we walked about 4 or 5 miles on the Asian side of Istanbul past midnight and had no concerns for our safety as were other people who were out enjoying themselves. The terrorist activity in Ankara recently is an isolated incident as far as I know and not a trend for which people think about. Whereas, I live in Minneapolis and safety and crime is at the forefront of our thoughts in our daily activities as there is gun violence, car jackings, illicit drug use & killings/theft is routinely reported in local news.
Earthquake prone zones- Regrettably, Türkiye is at risk of experiencing tremors/quakes in large areas of the country. Like California, they live with that risk knowing the big one could hit anytime and they accept it. In response to the 3 options you have, looking at seismic maps of Türkiye, it looks like Antalya - Manavgat is the safest location and the highest risk is Elãziğ. My mother has been living in Kusadasi which is a risky area and they experience tremors occasionally but life goes on. She has been there since 1997.
Kastamonu - I looked into Samsun which is 3.5Hrs away by car. In terms of weather, it is cool/cold in the winter and wet mostly. It is beautiful but what I observed was that the people were a bit more reserved than other large cities.
Elãziğ - I've never travelled to the eastern part of Türkiye and never considered it because traditionally the eastern part has not a focus area in development and have heard the people are conservative. Though they are very hardy and friendly people.
Antalya; Manavgat - Our biggest deterrent to considering Antalya is the hot and humid weather. We love colder weather which is one of the reasons we live in Minnesota. The cost of living is higher and it is a major hub of activity during the summer i.e. touristy. The Mediterranean coast is beautiful and has much to offer for traveling to the most gorgeous parts of Turkiye.
These are my observations and I suggest you research further to determine what's the suitable destination to meet your needs in Turkiye. Good Luck 😊