Änggårdsbergens Nature Reserve is a beautiful large green space in the middle of Gothenburg. For me, it is the second-best green area in town after Delsjöområdets Nature Reserve, but before the park Slottsskogen.
I can recommend entering through the Botanical Gardens, then you get to enjoy that on the way as well. Then simply go for a long walk, and if the weather allows, sit down and enjoy the views as you reach higher ground.