The Stadsmuseum (goteborgsstadsmuseum.se) provides a broad overview of the city’s history. Pass through the atmospherically gloomy Viking exhibition, which includes silver treasure hoards, weaponry and jewelry, as well as an original vessel, before learning about the founding of the canal city in the 17th century, livened up with some scandalous and amusing stories about the colorful characters of the era.
There's an entire section just for younger visitors, where they can ride a typical blue-and-white tram and climb the city towers. The Viking exhibition here always impresses school kids, particularly the remains of the Äskekärrkeppet, Sweden’s only original Viking vessel.