This Airbnb in Gamla Stan is one of the best I've stayed at in Stockholm. The setup of the apartment is a bit strange since you need to go thru the bedroom to get to the kitchen. But, with the bedroom and kitchen on the backside over the internal courtyards of the buildings, it is very quiet for sleep. The living room can get some street noise, but only from pedestrians and the often enough rolling bags of tourists.
I had some minor issues with a lack key supplies like toilet paper. But. the host quickly resolved it. At the time of my rental, the unit didn't come with laundry soap for the clothes washer. You might need to run to the store to get some like I did. Overall, I believe that if a unit comes with a washing machine, it should also have laundry soap.
The apartment was very clean and had everything you should need for a stay in the Old Town. I cooked a few meals while I was there and found the kitchen to be stocked well enough for a short stay.
The internet was spotty. It seems the host uses a cheap mobile service for the hotspot. Luckily I had my phone tethering as a backup. But if you really need solid internet, I'd check with the host to be sure it has gotten better.
Note that there are 3 flights of stairs to get to the apartment. It was on with me, but might be a bit much for other renters.
Overall, I'd recommend this great spot in the center of Stockholm. I'll stay there again if I get the chance.