Almost everyone I know who has been to Istanbul -- myself included -- lists it among their favorite cities in the world. Great food, beautiful architecture, fascinating history, and hammam: all not to be missed! I'll be there for my second visit in early November.
I did two food tours with Culinary Backstreets the last time I was there. They were both excellent, better than CB tours I've had elsewhere. I've booked another one for my upcoming visit.
Hammams range from super luxurious (with prices to match) to basic (also with prices to match). The one annemargaret recommended, as well as Hurrem Sultan Hammam (https://www.hurremsultanhamami.com/en/) are the very top end. The one I visited last time I was there was Kılıç Ali Paşa (https://www.kilicalipasahamami.com/), and I can't even imagine how those top-end places could be any better (but supposedly they are). I did a much more basic Hammam later in my trip in Antalya, and it didn't compare, but it was interesting to be in a place where I was the only foreigner. Still a nice experience. By the way, Kılıç Ali Paşa has separate hours for men and women (women during the day, men late afternoon and evening). Some of the larger ones have separate areas.
There's a separate discussion about tap and pay for public transportation in Istanbul (https://community.ricksteves.com/travel-forum/turkey/using-google-wallet-google-pay-for-transportation). You should get your answers there. If your credit card doesn't work, you should buy an Istanbulkart. Ask at your hotel where to get one.
Culinary Backstreets has both daytime and evening tours, but if 4pm is the time your plane arrives, you probably couldn't make it in time for a tour that evening. Maybe consider a hammam to help you relax after your flight, and a morning food tour on Sunday.