I've spent a lot of time in Stockholm and I don't usually stay in Gamla Stan, but truly, it is an excellent place to stay, especially for first-time visitors. There's a lot to do in Gamla Stan itself, but also it's easy to walk to other areas, such as Södermalm, and there's a tube that can take you all over Stockholm and environs.
It's worth keeping in mind that Gamla Stan is very busy and full of tourists, which also means that it's quite noisy. Also, this flat is right across from the German church, which has bells ringing many times a day. So either bring a sound machine with you, if you need white noise or similar, or be prepared for the sounds of street performers, drunk people, bells and so on.
The views from this flat are lovely and there is plenty of space. It feels quite homely. If I wanted to stay in Gamla Stan again, I would definitely return to this flat.