If you want to do more than just going out for an easy run there are some good options available.
Track runners might like Lidingövallen and Stockholms Stadion and those looking for a hill workout can go to Lidingöloppet 30km, Lidingöloppet 10km, Elljusspåret Gärdet, Norra Djurgården 3.1km or Lill-Jansskogen 3km.
If you want to test your fitness against local runners; the free group run Haga parkrun is available.
Running in a new city in the winter time can be tricky. Bad weather and darkness makes it hard to find good places to run.
For hardcore track runners who wants to workout on an indoor track; try Bosön.
Hagaparken is suitable for running year round and has electic lighting.
Elljusspåret Gärdet, Norra Djurgården 3.1km, Stockholms Stadion and Humlegården also has lighting and Djurgården, Lill-Jansskogen 3km and Björknäs Idrottsplats is usually usable all through the winter..
If you prefer trails you can check out Elljusspåret Gärdet.