Rosendals Tradgard. A cafe, a restaurant and a garden. I've been working here, sometimes I occasionally still do when I'm back in Stockholm. I love both the place and the people there. It's a fairytale world everyone should (no MUST) visit before leaving Stockholm. The atmosphere is amazing and you will forget when strolling around in the flowering garden that you're in the middle of a capital.
Forget Starbucks, in Sweden we got Espresso House which is waaay better. The milk is never (at least very rarely) over-heated and the coffee is always perfectly brewed. If you're hungry and on a budget: go here for their scones, cheap and yummy.