The great County Museum in Dorchester is very venerable and contains some wonderful collections. It could do with a little reorganisation, though, and is aware of it. The new archaeology gallery is bright and clear, very distinct from some of the older corners of the displays. The great central gallery is grand indeed and has the feeling of a big Nonconformist chapel or alternatively a market hall, and redisplaying that is going to require quite a bit of flair and sensitivity.
Lyme Regis Museum is on the site of the house of Mary Anning, the self-taught palaeontologist. Naturally fossils are very prominent in the branding, as they tend to be all along the Jurassic Coast. I'd forgotten how the museum galleries open off this dramatic spiral staircase which, for some unaccountable reason, sports a marble bust of Lord Byron. It was all very well until about 250 German teenagers turned up (there can't have been 250, but it felt like that), and the space was rather transformed as they all tried to negotiate their way around via this staircase.
Bridport Museum is free to go in and is also very pleasing indeed. The whole display space was refurbished a couple of years ago and is bright and considered, giving an insight into the life and history of the town that impresses with its clarity and concision. I really enjoyed walking round it again, as it was so transformed from my last visit.
Finally, Sherborne is a small and quite traditional museum near the Abbey. There's a lot going on inside and a clear narrative about the town is elusive, but as always many of the objects charm in their own right. One up-to-date item that has been installed is a virtual edition of the Sherborne Missal which allows you to turn the pages and focus on different elements. Not every page is included (that would be a lot to ask) but you do get the famous vignette of St Juthware having her head cut off and then carrying it to the altar of Halstock church.