Here is a great way to explore a town just outside of Stockholm and it is full of interesting history and sights to see. My family lives in Uppsala so I have experienced many of these items highlighted. Uppsala is about 45 mins away from Stockholm so it makes it a great addition if you can spare a few nights and don't want to travel far.
This itinerary was a FAM (Familiarization) trip prepared for Travel Advisors. These itineraries are often jam packed with experiences because the tourism board wants the advisors to experience as much as possible. I don't recommend doing all the activities in the same day like they suggest. You can use it for inspiration and pick and choose the activities you are interested in or add more days if you like to do it all!
This is just one example of an itinerary I could prepare for you. It is fully customizable to suit your specific travel desires. I am a Sweden Specialist and I have traveled to Sweden over a dozen times. Also review my Sweden Archipelago Vacation example itienrary for more ideas!