Kuressaare, the largest town on Saaremaa, is actually quite small and perfect for a walking tour.
The county museum founded in 1865, is located in the bishopric castle. There is a large exposition of the history and nature of Saaremaa; about 30 art, history etc. exhibitions a year; concerts of classical music. In the summer season you can rest your Iegs in the Tower cafe, look at historic ashlers in the cellar and buy pieces of Estonian art and handicraft or enjoy the concerts of "Castle Summer Music".
Sightseeing in Estonia | Interactive Map | County of Saaremaa