The most important thing: Asparagus Hotel is walking distance to the Blue Mosque, the cistern, etc. It allowed us to get up and wait in line early before the morning rush of tour groups. It's also close to tram. It you're not in a rush, keep walking to the spice market and Grand Bazaar. The neighborhood is safe. In the tourist area, there are a million people in your face all the time.
Also you cannot beat the price. We have a studio on the top floor. Great windows on two sides of the room--just like the picture. I can see the water and a small mosque. The suit is equipped with hot plates, refrigerator, air conditioning, free WiFi, free water, etc. For the price, I doubt I could do better. The staff were friendly and polite. The manager was prompt with Expedia/WhatsApp messaging. It was a nice authentic experience. Warning: the streets are cobblestones and a bit uphill. No elevator.