In Gothenburg there are many interesting museums - a number of them where you can spend a whole day. For the younger crowd, Universeum and the Maritime Museum are popular, but the Museum of Art and the Museum of Gothenburg have displays that suits both young and old visitors.
Another favorite in the rain tends to be shopping and in Gothenburg there are several large shopping mall. Nordstan, NK, Arkaden and Kompassen are all in easy reach of each other in the city center.
Between museums and shopping you might want to sit down and give your legs a break. The café culture is spread all around Gothenburg and it’s always easy to find a hole in the wall café like Bar Centro or a more classic one lika Café Kringlan and Café Husaren in the Haga area. Also the market hall Saluhallen is a great tip when it rains. Take your time and grab a lunch at any of the restaurants or just enjoy the atmosphere.