I spent two weeks in Stockholm, one of them dedicated to visiting the city. Here are some notes that could be useful for travelers. It is not at all exhaustive though, but just the result of my tastes and peregrinations. I would appreciate to know if you think I missed interesting places!

If you are in a hurry, my top 3

• Östermalms saluhall;
• Nordiska museet after 13 o'clock;
• Historiska museet.

General tips

• 1 EUR $\approx$ 10 SEK, local currency can be withdrawn at the airport (and at least with my bank, it is cheaper to withdraw directly in SEK rather than accept the offered conversion in EUR, which includes a significant change tax);
• "Hello" = "Hej" or "Hejhej", pronounced not too far from the american "Hey"; "Thank you" = "Tack", but almost everyone is willing and able to help in English anyway;
• Museums have a tendency to open late (10-11 AM) and close early (4-5 PM);
• Single metro tickets bought at machines in metro stations are very expensive (45 SEK). If you buy one anyway, you obtain a paper ticket that you are supposed to show to the clerk to enter the metro. It is cheaper to buy a rechargable card for 20 SEK (lasts for life) at the counter and charge it with trips.
• Some metro stations are really pretty. But in general I prefer walking, which is especially suitable in Stockholm since the city is not too large. Walking is also the only way to stumble on random places that one wouldn't have discovered otherwise. Be aware though that Stockholm is a relatively hilly city and some of the paved streets in the old city are in a rather poor condition, so good shoes and a good physical condition are appropriate.
• Stockholm is spread over a handful of islands of different sizes and ambiances, whose main ones are:
  • the continent,
    • Kungsholmen ("The King's islet"), where my hostel was, but not the island that I found the most interesting,
    • Gamla Stan (the old city) with the King's palace, a lot of old paved streets, tiny passages and many tourists. Consequently, it is not the place where the food is the cheapest.
      • Riddarholmen ("The Knights' islet"), a small island with mostly administrative buildings and courthouses, but it is prettier than it sounds,
    • Skeppsholmen ("The islet of the ships"),
    • Djurgården ("The animal park"), also nicknamed "museum island",
    • Södermalm.

Points of interest

Continent

• Historiska museet Museum of the history of Sweden, free and interesting;
• Östermalms saluhall Covered market, closed on Sundays. It is a very nice place to buy all kinds of fancy food (fish, meat, bread), and also to eat traditional Swedish meals that can be heated up and served on the spot. It is in a temporary location until winter 2020, while the historical building is being renovated. Without contest one of my very favourite places in Stockholm;
• The observatory hill Nice point of view to see the sunrise over Stockholm;
• KTH library seems open to everyone, is a pretty nice building and is a nice place to study, or prepare the rest of the day;
• KTH R1 The dismantled (and safe) remains of the first nuclear reactor in Sweden. It is now used as a culture center and exhibitions and parties are regularly organized there.

Kungsholmen

• The city hall is open to visits during the summer, but the view from under the archs is very pretty all year long. This is where the Nobel gala dinner is served on December 10th. Fun fact: the restaurant is open all year long and can serve the menu from any given year's gala, on the porcelain actually used for the banquet.

Gamla Stan

Not my favourite part of the city: too many tourists.

• The royal palace, the official residence of the royal family (but they don't usually live here) can be visited. As for the city hall, it is a massive building but finely decorated inside. Watching the changing of the guard in the palace's courtyard is a fun attraction;
• The Nobel museum was a little bit underwhelming but I probably had too high expectations. It is rather small, presents two showcases about Alfred Nobel, a temporary exhibition and a permanent collection of some of the personal items that the Nobel laureates are invited to donate to the museum. Among them, the scarf that Malala Yousafzai wore during her speech at UN, Geim and Novoselov's original scotch tape dispenser, or the sample jar Barry Marshall drank his Helicobacter pylori broth from, but also a trumpet, a calculator, an abacus belonging to the laureates… Most notably, some of the prize diplomas were also exposed. Each of them is unique, and are expectedly some of the finest works of art there are, drawn and colored by hand by Swedish artists. They also have a video room with short introductions to the work of the laureates playing in random order: I could have spent hours in this room…

Riddarholmen

• Riddarholmskyrkan The visit costs a couple dozens of crowns, but I recommend it. This church is the sepulchre of the royal family. It is better to see it after the visit of Historiska museet to have some of the genealogy in mind (it doesn't help that everyone is named Gustav).

Skeppsholmen

• The museum of east-asian art: free and open late (20 o'clock). I have seen a nice exhibition on traditional paper making in asian countries, and the Japan section of the museum appealed to me. The museum also hosts an extensive collection of ancient chinese books (not that I could read them);
• Moderna museet that I didn't have time to visit.

Djurgården

• Nordiska museet: go in the afternoon, it is free after 13 o'clock. This is the museum of nordic life and exposes the daily life of Swedes during the last 6 centuries. The building itself looks like a fairy tale castle. Really worth the visit;
• Vasamuseet exposes the local Titanic: a battle ship that sunk in 1628 in her maiden trip and was resurfaced in 1961;

• Skansen is an old and large open air museum / ecomuseum / zoo. The public is mostly Swedish: families, or school classes. I understood that Stockholmers generally buy a ticket allowing entry all year long, and come back regularly for the animations proposed all along the year around the traditional holidays. I visited over Easter and have seen for example a Swedish grandma prepare traditional Easter cakes. Furthermore, the shop is nice, and there is a couple of restaurants and hot dog stands inside: I would recommend to visit Skansen in the morning, eat there and wait for 13 o'clock to go visit Nordiska museet just in front;
• The botanical garden was unfortunately closed for restauration.

Södermalm

• This part of the island, besides being a nice picnic place, has very old traditional wooden houses once occupied by the working class. The view from this bank to the north side of the city is alone worth the trip;
• Stockholm's city museum, closed for restauration until a couple of days after my return date…

Further

• The furthest I went by foot is Vinterviken, a very bucolic place once owned by Nobel where he installed his dynamite factory. The beauty of the landscape contrasts with the rocks torn by the experiments. The place seems to be appreciated by Stockholmers since I saw many of them jogging in the park, or going out with a baby stroller. The old acid factory was converted into an exhibition center, and a really nice restaurant. You can take a tray, order one of the three meals of the day, grab bread and water and go eat it outside at one of the picnic tables, as a reward for the walk to arrive here from Stockholm. I warmly recommend it.

Even further

• I wish I had the time to go pick a rock at Ytterby's ytterbium quarry but that will be for another time.