Baliol's castle on the River Tees. Very nice keep tower overlooking the river. The castle is at one corner of a very attractive market town, which is worth visiting for its own sake, with some fine old slave-labor mills on the other side of the river from the castle (although they might have torn these down since I was last there -- they were derelict).

(I include Castle in the title, because the town itself is called Barnard Castle, not just Barnard.) It was years ago since I was there, but I hope the derelict mills stayed up long enough to be caught up in the preservation / industrial museum movement that became popular in the 1980s-1990s. In some ways they were more interesting than the castle, fine as that is.