Rosendal Palace, a small summer palace from the early 1800's (this can also be visited during the summer months). The gardens are located just adjacent to the palace and were started back in the 1860's as a greenhouse and gardening school. Since the 1980's the gardens are run as a foundation and their main purpose is to spread information about biodynamic gardening and the farm-to-fork concept.
Rosendals Wärdshus which is located just on the grassy hill above the gardens. Swedish cuisine with great picnic options as well. My visit there.
Rosendals Trädgård is located on the island of Djurgården, near many of the main attractions like the Vasa Museum, ABBA the Museum and Skansen. This makes it sound like it is easy to stumble upon, but it is located a bit inland from the attractions and requires a 15 minute walk or so from these attractions. But it is a beautiful walk through the park & forest. If you are taking public transportation, you can take the Djurgård tram to the stop Bellmansro which is about a 10 minute walk from the gardens. The easiest way to get to Djurgården from the Rival Hotel is the Djurgård ferry from nearby Gamla Stan, after which you can either walk to the gardens or take the aforementioned tram.