Its not on the course, but Harlech Castle looming over the course has to be up there for one of the best off course objects.
Old Joe on the edge of Edgbaston is very cool.
In fact, the clubhouse at Edgbaston is VERY cool.
Though already mentioned, Burnham's church and Pennard's castle are very fine. Bill, an excavation done several years ago found evidence of a small village around Pennard Castle.
Ciao