I'm not sure what "Inn" tour means, but I did go to Blackbeard's castle years ago. Great view, but otherwise boring. It is just a very old tower. They do rent out rooms...I think there is one room on each level and about 4 levels. But, all we got to see wass the entrance, which is an open air passage through the middle. Too many other things to do there.
Just my 2 cents