The Balaton Museum tells the story of Lake Balaton and the country around it, from natural history and wildlife to Roman stones, medieval finds, and local art. The Neo-Baroque building is a useful counterpoint to Keszthely's palace: smaller, quieter, and focused on the lake itself.
It is a good stop if you want context before travelling around the western end of Balaton, especially on a rainy day or between walks along the waterfront.