One full day in Stockholm next summer

If I was in your situation the armoury (Livrustkammaren) would be the last on the list, the Vasa museum and Livrustkammaren would be a lot of military history for one day and I would suggest something else instead.

My "must see" museum in Stockholm is Skansen. I could spend an entire day, there...in fact, I have - more than once.

I would say the Vasa Museum is the best. The site is lovely, the exhibits are well done and the story a reminder that large defense project screw-ups are nothing new! The nearby Nordic Museum is large - I’d check for specific exhibits. I saw one on “light” including a “Northern Lights experience,” and one on Sami culture - the latter, I think is permanent. I skipped Skansen because of the rain but rode the bus all around Djurgården. I skipped the royal stuff and found the Nobel museum underwhelming and City Hall more interesting than expected.

My second favorite stop was the Fotografiska on the edge of Södermalm directly across the water from the amusement park on Djurgården. It is (or was in 2017) a wonderful venue, with excellent exhibits, a small performance space, a terrific shop, and a nice cafe. It’s not in the book - I happened to spot a flyer in the train station for an interesting exhibit and was very happy I did. It’s reachable by bus or walk from Slussen at the “foot” of Gamla Stan. Photography only.

I would visit VASA Museum, the City Hall( take a tour to see it’s amazing interior), and Drottingholm, a short and lovely boat ride away to see the Palace where the royal family lives. Walk around Gamla Stan. I strongly encourage you to add more than one day to see this beautiful city. We were there five days and could have spent more time.

We were there last year. The Vasa and Gamla Stan walk are enough for a day. Perhaps add the city hall tour. A boat trip to Drottningholm and back is too much to add on in a day.

If I had only one day in Stockholm, I'd spend most of it walking around Gamla Stam, visiting the palace, etc., and then seeing part of gamla stan on Sodermalm to include walking Monteliusvägen for the view. Then I would take the ferry to Skansen for a sense of old Sweden throughout the country, and then the tram back to near Gamla Stam, and then I'd have a sit-down at a restaurant terrace on the harbor. With so much to see in this beautiful city, I wouldn't waste any time in an indoor museum, especially for a museum about a ship that couldn't float (IMO, YMMV). Make sure you have a piece of Prinsesstårta and a Kanelbullar, probably not in that order.

On Djurgården Island , the King’s former hunting grounds, you will find VASA and several other museums. We stayed on that island for five days and enjoyed it. There is a little ferry that takes you over to Gamla Stan.

We spent a full day at the Vasa Museum and walking Gamla Stan. The area around the Vasa is fun itself, we took a ferry, walked miles and bought salty licorice. We intended to get coffee and cinnamon rolls I think they were, but saved the $ for smelling salts. Beautiful city and a very nice day. The cruise into the city is beautiful so rise and shine.

We did Stockholm last year and recommend a walking tour around Gamla Stam and going to the Vasa Museum.

History is a top priority for me. I was there in October so most things opened around 10:00 and closed at 17:00. I was by myself so I just grabbed bites from museum cafes and vendors. Perhaps in summer opening hours are longer. I think with one full day you could do 3 or 4 of these if you like to keep moving and are organized: Vasa, history museum (see only the best parts which are the gold room and bronze/iron age exhibit, small Battle of Gotland exhibit was interesting), the armoury, and art museum, in order of preference. The Storkykan church with the St George and the Dragon statue is very near the armoury. Skansen was great but it just didn't do much for me. I normally love open air museums but I think it was partly the sense that it's a large thing to see and I had limited time. Vasa is perhaps 3-4 blocks from the Swedish History museum. BTW on the history museum website https://historiska.se/exhibitions/ it says "the world's largest Viking exhibition opens in in early 2021". Maybe that will rearrange priorities!

In 1 1/2 days in Stockhom in October I did this:

Arrived mid-morning from the U.S, ready to roll by 11:00. Ferry from Gamla Stan to Djurgarden, which provided great views of the city over the water on a brilliant Fall day. Strolled around Skansen for a few hours grabbing little snacks like cinnamon bun and looking at old vernacular architecture and interiors. Walked to Vasa museum for the remainder of the afternoon. Vasa is a can't miss for me The restored ship is an amazing sight at it's full height and seemingly near-perfect condition,. Additionally there are several floors of artifacts found with the ship that provide insights into the period and life on board. The English language tour that walks around the ship and points out detail is also very good.

Second almost full day:
Looked at my itinerary and decided the thing I wanted to do most was see the Vasa again when I was a little more awake! Then maybe 4-5 block walk to the Historika Museet. The Gold room Viking and medieval gold and silver displays were really incredible and provide insights into trade and money. The cozy cafe has fresh open sandwiches and other options. The Stone/Iron/Bronze age exhibit was well done. It was cool and steadily raining so lingered too long at the museum on some less outstanding exhibits. Took the tram line to Gamla Stan, to the Stockholm Medieval Museum. It's a new-style museum that doesn't have a lot of artifacts and uses dimensional displays such as partial mockups of houses. I thought it was just OK and would skip it next time. Passed the armoury with regret because it was getting late and went to the Nobel museum for a change of pace. It's not a large museum but provides a great perspective on the scientific, literary and social developments of the last century plus. Probably spent 90 minutes there including fika break. By that time things were closing and I walked around Gamla Stan.