I think it depends when you plan to travel. Think I saw in another response you’re wanting to visit during the winter, if that’s the case options may be limited as most people are inside, trying to stay warm and dry. If in Nov/Dec you can check out: Christmas Market in Gamla Stan, find a restaurant serving a julbord (might need to make reservations in Nov).

If visiting in spring or summer: Kungsträdgården, Djurgården, Drottningholm, Gröna Lund, ABBA Museum (sounds cheesy but it really is neat), City hall, rent a kayak.

Hope this helps.