If you do one thing in Stockholm, go to the Vasa ship museum. An impressive story of a ship raised up from 30 meters under Stockholm Harbour after 333 years under water, from 1628 to 1961. its been put back together and restored and is now enclosed in this museum to explore from 5 levels around its perimeter. It is 98% original and even more impressive in details. There are actually some really neat exhibits around it with small scale models, a cross section, the captains quarters, an informative and worthwhile video, and model renditions of what the people of the ship would have looked like after their remains, belongings and teeth were analyzed. Neat stuff!!
If you do 2 things in Sweden, not including wandering the streets of old town, you need to head to Skansen. An outdoor open air museum which is like Scandinavian Disneyland where there are sections for old mid 19th century farms, an old town, zoo, aquarium, and many other buildings set up as to the date of existence. They even had real people dressed as per the times to chat with and ask questions. A cute little place especially cool of you have kids.
If you do 3 things, rent a bike at the edge of the island near both of these museums and spend the hour riding through the tree lined paths, checking the seaside view, and resting your butt and feet while riding or on a park bench watching baby ducks, to prepare for the 3.5km trek in the hot sun back to the hotel area. For dinner we found Italian, the go-to meal for really hungry people, (mine with fresh mussels and shrimp), before crashing for a long sleep on one of the hardest beds possible, short of staying at the ice palace! We did not make it to the icebar however, as baby induced zombie status took over by 8pm. It was another long day on the feet, probably 10km walking and an hour bike ride in hot weather! Phew.