If I'm not mistaken, the Hotel Du Chateau is just adjacent the old Cite walls, no?

If that is the one than it has a very good reputation for service and ammenities, albeit I haven't stayed as a guest.  

The location cannot be better,the entry gate to La Cité Médiévale must be just a few minutes away.  

The newer city or Ville Nouveau will then be 15mins walk over the Pont Neuf so very close. Carcassonne is a small walkable town with excellent restaurants and historical sites.  I think the location of the hotel cannot be better!

In case you are looking few more recommendations, on restaurants and landmarks, checkout my Carcassonne blog post:http://www.aforkinlondon.com/post/89990427830/carcassonne

Hope this helps!