Skeppsholmen was the navy's island for three centuries, and when the fleet left, the art moved in. It's a short, water-wrapped loop with the best long view back to the Old Town — and an afternoon walk, because the light wants to be behind you when you look across.
From Kungsträdgården it's a few minutes to the Skeppsholmsbron, where the gilded crown on the bridge railing is the first photograph. Over the water, the Moderna Museet and ArkDes share one low Rafael Moneo building — modern art and national architecture, both free to the collection, both shut on Mondays, so plan around that. Down at the southwest shore the af Chapman, an 1888 full-rigger turned hostel, stands rigging-against-skyline.
Then south over the little bridge to Kastellholmen, which almost no one bothers with — a toy citadel, a flag, benches facing the bay. Come back the way you arrived and finish at the Nationalmuseum on Blasieholmen, reopened in 2018, right on the quay. Coffee in the courtyard, then the short walk back to the T-bana.