Scandinavia has been on my list of travel wishes for a while now and I'm considering a trip to Stockholm in June.
I'll only have a week, so I'm wondering if it's feasible to include Oslo or Copenhagen into the itinerary. If not, are there other must-see cities in Sweden that I could see on a day trip from Stockholm?
Maybe a lot of people will disagree but in my opinion, there are no must-see cities that you could squeeze in during a day trip from Stockholm. There are however small cities, castles, the archipelago, countryside and so on that you could visit during a day trip. Apart from Stockholm, I would say that Gothenburg and Malmo are the more interesting cities - non of them suitable for a day trip though unless you fly. Same goes for Dalarna County (moose and bears in amounts), Kiruna (northern lights and midnight sun) or the beautiful island Gotland (wonderful during the summer, with seastacks and other amazing scenery).
If you go to Malmö, Copenhagen (capital of Denmark) is really close. Just 40 minutes away by train definitely suitable for a day trip. And Oslo in Norway is a really small town, so trying to make a day trip out of it is no problem - apart from the long travel time. :)
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If you are in Sweden any time June19th to 21st, it will be Swedish Midsummer. Basically Summer Solstice. A cool place/ the holy grail of this this celebration is a small town called Leksand. It's about a 2.5/ 3 hour train ride northwest of Stockholm.
I've lived there the last 4 summers. They have a big grass pit where you will find (weather permitting) about 25,000 people celebrating like there is no tomorrow. Lots of people will be wearing old-timey traditional clothes from back in the days, which is cool to see. They do a "raising of the may-pole" in the center of the pit and then everyone does a traditional dance around the pole once it is fully up. It's awesome. The Friday afternoon of that weekend is when all of that takes place. It's a sacred time for all of my Swedish friends and I think worth taking a look at if you're in the Stockholm area. :) Probably one of the most authentic Swedish experiences you could come across, period. Let me know if you would like more details!
Stockholm is very far north. It would probably not be a day trip however, I would recommend going to Copenhagen. Denmark is a beautiful country and the museums are superb. I hope you have fun!