There is no landing fee. But if you park near The Squadron who run one of the cafes, they try to imply that you should pay them something. There's another very good cafe on the other side of runway 31 near hangar 4 where you can park for free.
Lots of interesting vintage aircraft use NW, but some are totally inaccessible and others dont encourage visitors to their hangars. So if Thing is visiting just to get close to old aircraft then NW may not be as good as he would wish. Still a great place to visit though.