The former house of Prins Eugen sits right on the water, with a fantastic view over Södermalm and Gamla Stan. The view itself is worth the 20 minutes of tram (line 7) and the additional 5 minutes of walk.
Best of all, the gardens are open to the public and you can soak in the views from there.
A visit of the manor and its collections takes about 90 minutes. The manor kept its original decorum including paintings from the great early 20th century swedish painters of Carl Larsson and Zorn. Some of Prins Eugen artworks is there as well.
The art gallery houses mostly temporary exhibitions, so check the program in advance.
If you are looking for a real introduction to Swedish art, aim for the Nationalmuseet. But Prins Eugens Waldemarsudde is worth a visit for the combination of art, history and views.