It would be fair to say that the whole of Hadrian's Wall by virtue of it being a World Heritage Site is technically a Site of Interest, however there are places along its length (and close to it) that offer good reason for further exploration.
Some of these places have free entry and others have a cost element. It's also worth noting that not all of the Sites are open or accessible all year round, so it's advisable to check opening times before you come.
English Heritage Sites
Vindolanda Trust Sites
Tyne & Wear Museums
Walking Considerations -