If you want to do more than just going out for an easy run there are some good options available.
A short trip away you can find the tracks Stora mossens IP and Sätra IP that should be open to the public and those looking for a hill workout can go to Kärsön 1.8km, Solviksspåret, Åkeshov 1.55km, Fornstigen 18km or Skogsrundan 3.3km.
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.
If you prefer trails you can check out Kärsöleden 6km.