From a quick search, I think there's a large Iranian population in Gothenburg, so I would surprised if there was not at least one mosque in the city (although expect it to be in the outskirts or suburbs).
Wearing a hijab in Gothenburg is completely safe, Swedish law does not prevent it. You won't have some form of religious police arresting you for wearing it, that's for sure, sister.
Hope you enjoy your time there. And remember to wrap up warm!