If you want to go out into nature inside the city limits, there are many possibilities in every direction, but if you take bus number 3 from the centre and head southeast towards Hervanta, you will end up by the beautiful small lake Suolijärvi, which has a sense of wilderness in it. There is a public sauna & hole in the ice throughout the whole winter (check FB) and there is a good, wide path to jog or to ski on.
But what I like best is the small trail that goes around the lake following the very edge of the water. Of course, during winter, it can be a little challenging to find the little bridges that go over the wet parts when the snow covers the way and the ice is not thick enough. You should always wear good shoes and be sure you will make it during the sometimes short daylight. You can’t get lost if you stay on the shore just by the lake, but there are certain parts where the little trail crosses over the bigger path a bit further from the lake. From there, you just need to remember to turn back to the shore.
It takes about an hour or more to walk this 6-kilometre trail with such lovely scenery: swamps, forests, hills and water… You can take something to eat & drink along the way and take your time exploring the nature that changes as you walk along. I like to do it clockwise.