I highly recommend this jewel, located on an historic street, within walking distance from most of the tourist sites you'll want to see. You'll always find your way back, because the tower can be seen from anywhere, and, if you're tired of walking, you only have tell the taxi driver, "Galata Tower" and you'll be dropped off 40 meters from the apartment (usually less than 20L).
Inside is cozy, quaint and clean. The host's description is spot on, so no need to repeat them, and every little detail has been thought of, from soft towels, to playing cards, to laundry soap.
If you've done some research, with the location and amenities (even a clothes dryer), this is not over-priced. The hosts answer all requests within minutes (truly a super host). I would suggest accepting the offer of the airport transfer. Sure, it costs a bit more, but you don't have the hassles of a shared ride, or trying to say where you want to go at the airport, and it's a trusted driver.
I will not even look for a different place on my next visit.
Things to consider if you are older: stairs. The good reviews below I consider accurate.