If you want to do more than just going out for an easy run there are some good options available.
Parkruns are great ways of meeting local runners while also getting a great workout in. Haga parkrun is not to far from here.
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.
Norra Djurgården 3.1km has lighting.
Lidingövallen is a popular place to run in this area.