7-day trip and the plan is to make stops in Istanbul, Izmir, and Cappadocia
Dear Serena, totally no worries. The only place where you might noticed it is at its border and Turkey is a very very big country.
Apart from that Turkey is a very safe country also for women.
Have a great time and wonderful holiday!
You don't need to worry one bit.
The only area of Turkey that feels the conflict is The Hatay region where Antakya is, which is next to the syrian border and refugees are crossing over the border, but that is hundreds of miles from where you are going and places like Cappadocia Istanbul and Izmir do not feel this conflict directly.
I have been to Turkey dozens of times and have lived and worked there and I can assure you that you will not have to worry about your safety regarding that matter.
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You are going to visit places very far from Syria. (Cappadocia, the closest is 10/11 hours far by car).
I just came back from a trip around Turkey with my girlfriend, and a place we visited was Sanliurfa, 50 km far from the Syrian border, and even if we got even closer, no problems at all.
Just don't forget you are traveling in a Muslim country, so bring with you a scarf, to be able to visit mouques, especially in Istanbul, are amazing.
Hey Serena, you don't need to worry, especially not when going to Istanbul, Izmir, and Cappadocia. You will be far away for the risky areas. Enjoy your trip.