I am S, F, solo, 70+ and will be in Istanbul in November. 99% of the time I use booking.com for apartment stays but thought I might be better with a hotel/concierge/front desk/etc. Have been to Istanbul in 1986 so really will be new to me after so long. Would like to stay in the $100 or less range.
I was in Istanbul in 2007 (some time ago) as a solo female older traveler (52 at the time) and had no problems with safety issues. I stayed in the Sultanahmet area, which is the historic center and good for being close to the major sights, like the Blue Mosque and Hagia Sophia. I felt very safe here and liked being able to walk to so many places.
You also might search for other threads here on the forum. For example, here is is a thread discussing hotels for someone with an older mother, wanting concierge service: https://community.ricksteves.com/travel-forum/turkey/sultanahmet-5-day-visit-for-92-yr-old-slow-but-capable-mother-with-mid-age-sons
Edit: For what it's worth, I stayed at the Hanedan Hotel in Sultanahmet, and found it quite nice and very reasonably priced. Keep in mind I was there in 2007, but I know the hotel is still there, so you might want to check it out. The owners were very nice and helpful, and I felt very safe there. And I loved that you could eat breakfast on a lovely roof terrace overlooking the Marmara Sea.
There are plenty of lower budget hotel options in Sultanahmet area, as well as the area near the north end of the Galata bridge. I stayed in both areas and felt quite safe. One hotel (Agora Guesthouse) was lower budget and had front desk staff but no "concierge" services. I used Booking.com to arrange it - just note if you don't pay in cash there is a credit card surcharge. Great location and rooftop breakfast room had views of Blue Mosque spires, 5 minute walk to Hagia Sofia. The other (Galatas Hotel) was higher end (on a RS tour) with fully staffed desk and nicer business style accommodations.
With the highly variable Turkish currency, what might be the equivalent of $100US today could be drastically different 11 months from now. No way to predict.
Exactly what I was looking for and already made a booking, so thank you.