Mathias Dahlgren's Matbaren
If you could only visit one restaurant while you're in Stockholm, this is the one to go to. The restaurant is called Matbaren (literally "the food bar" in English) and is owned by one of the best chefs in Sweden, Mathias Dahlgren.
Mathias Dahlgren has two restaurants next to each other, which can be a little bit confusing, called Matsalen (literally "the dining room" in English) and Matbaren. The first having two Michelin stars and the latter having one. Although I much prefer Matbaren! It's actually one of my favourite restaurants in the whole world.
The restaurant serves amazingly great food based on what's currently available in Sweden and other parts of the world, and they do it perfectly. To me this is the best representation of what Swedish food can taste like (and should taste like). Whatever I order from the menu, I know it'll be fantastic.
The atmosphere is relaxed, warm and pleasant which matches their concept perfectly. You order smaller dishes, one at the time, and finish your meal whenever you'd like to. For me two dishes and a dessert (of course) is usually enough.
You can't leave this place without having dessert. And coffee or tea! Together with your coffee or your tea you'll get the best Madeleine cookies you've ever tried. Believe me. I've lived in Paris for a couple of months now and I've never tasted any Madeleine cookies better than the ones at this place.