Hi there ! Swedish people often warned foreigner that Spring really comes in the end of April or at the beginning of May. Swedish Spring in Gothenburg/Göteborg is mostly a drop of luck between rainy day (sometimes hail), cloudy day or sunny day !
If you want to enjoy the nature in Gothenburg take the direction to the park, Slottsskogen (tram stop: Linnéplatsen). Slottsskogen park is not really far from the city center and just in front of the Botaniska garden. In the park there is a nice zoo with pinguin, moose, poney, rabbits, swan and even more animals to go see. The park is really vast so be sure to check a map.
Spring time is launched by the apparition of the nice and beautiful cherryblossom flowers. The city of Gothenburg celebrate the beginning of spring with an Hanami in Slottsskogen park and different events such as a parade, concerts and markets. It is also a really good time to go study outside, on the grass under the sun. You can also take a fika and sit on a terrace and enjoy a nice kanelbullar with the sun.