Jönköping is situated at the southern point of Lake Vättern, and the paths around the lake are a great place to go for a walk.
From the train station I walked on the west side of the lake on the path there - going past a small stretch of 'beach', through lovely areas (like where the bridge is in the second photo) and into where there was housing with great views over the lake and of the city.
There were a few other people out walking even though it was fairly cool. It makes for a nice walk and there are one or two small hills to go up or down, but don't worry there are also a few seats along the way if you feel the need to sit down, or just to enjoy your surroundings!
Jönköping, at the bottom tip of Lake Vättern, is a good vantage point. At the train station, you can cross the overhead bridge. This will bring you a long walking / biking trail that goes for a bit around the lake.
It is the prettiest in the morning, especially on days where the skies are clear. Swedes like to sit out and enjoy the good weather.
It is a very nice walk! Tell me if you enjoyed it :)