I've been digging up information for my daughter because she likes to run, and we will be in Stockholm in July, so I've been finding some areas for her to run. Sandanciso, who is a frequent poster here, told me about the island of Djurgården. There is a national park there with walking and biking paths. She said she runs there a lot and it's really beautiful. My daughter plans on going there to run. Plus it's very easy to get to from the city center. You can get there by public transportation, using bus, tram or ferry.
https://www.visitstockholm.com/stockholms-districts/djurgarden/
https://www.nationalstadsparken.se/
https://royaldjurgarden.se/en/en-gron-oas/
Just one word of caution. I was also looking up information about the Archipelago. There's a lot of hiking trails there, and I think that was mentioned above. One of the things I found out was that the area has a lot of ticks, and many of them carry encephalitis, and of course Lyme Disease. If you're planning on doing a lot of hiking while you're there, I would strongly consider getting vaccinated for that. https://www.cdc.gov/tick-borne-encephalitis/data-maps/index.html
Here is the information from the Archipelago website that actually mentions this as well: https://stockholmarchipelagotrail.com/questions-and-aswers (scroll down to "Dangerous Animals)
In the Stockholm Archipelago, we are fortunately spared from dangerous animals. However, you should be careful not to step on a viper (adder), as this would require medical attention. The most common nuisance in the archipelago is the tick. They are found everywhere, and you should make sure to remove them as soon as possible. If you are not vaccinated against TBE, we strongly recommend that you get vaccinated. Ticks can carry Lyme disease and/or TBE (tick-borne encephalitis).
