Stomboli is an interesting trip,if you want to walk up to the crater (or you can even watch the eruptions by night,from a boat trip).
Nicest for swimming and beaches is maybe Panarea,though it is expensive..the beaches in general are not good on the Aeolians,and the sea water quality is very variable.But there is sea all around,some good swimming (often from boats rather than from land).
Best mud baths are on Vulcano,and there is also a nice volcano climb there,up to the crater.