Local Museums:
Radstock Museum – local mining museum
Frome Museum – local history
Somerset Rural Life Museum – Glastonbury
Haynes Motor Museum – wonderful collection of vintage cars
Roman Baths, Holburne Museum Bath
Jane Austen Museum Bath & No.1 Royal Crescent Bath
Stourhead House
Longleat House
A detailed list of Somerset Museums can be found here: https://en.wikipedia.org/wiki/List_of_museums_in_Somerset