Sochi History Museum is one of the city's older cultural sights, with collections that range from archaeological finds to natural history and the development of Sochi as a Black Sea resort. It is a useful stop if the city otherwise feels like beaches, promenades, and Olympic infrastructure.
The museum is not huge, but it gives helpful context for the coast and the mountains behind it. Allow about an hour, more if you read Russian or want to work through the exhibits closely.