It depends a bit on what you're looking for and what you are interested in. What brought you to Stockholm? You mentioned day trips in the other thread, anything particular you're interested in?
The Vasa museum is a great museum and well worth it in my opinion. The Abba museum is a bit of a hit or miss, great place if you're a fan but maybe not worth it if you're not a big fan. Skansen can also be a great place to learn bit about Sweden. And there are many more museums. Gamla stan is worth a bit of time just walking around. Västerlånggatan is a bit touristy and can be crowded, but step away from it and the crowds can be much smaller. Just beware of the restaurants in Gamla stan, don't visit them without checking the reviews, there are some great ones there but also many tourist traps.
Any particular kind of island you're looking for? There are around 25000 islands in the Stockholm archipelago so you have a couple to choose from. For a short trip to get a small taste of the archipelago, a trip to Fjäderholmarna to have lunch is a good option. Or you can spend a couple of nights in the archipelago. Public transportation in the archipelago is operated by Waxholmsbolaget, www.waxholmsbolaget.se. Route map: https://assets.ctfassets.net/4l7cjdaypzcu/UrqsczDUUVXP3wS6rUTqF/084204d2cbb11957c0992e8fb7f3ac28/linjekarta-waxholmsbolaget-maj2025.pdf
And for hiking there are many opportunities, there are many trails in and around the area. Depending on how far you want to hike.
