Forests & lakes, Göteborg
Well, maybe not quite in the city, but not too far out either!
The Delsjön area is designated park area for hiking, biking and sporting, but also for canoeing, beach life and relaxation. There are hiking trails around the area, and a few places good for swimming too. Many locals come here for the day to enjoy the nature, the local wildlife (yep, we saw a deer when we were here the last time!) and the lake (Delsjön).
Access to the area is free, and there are good maps around too.