HBO is doing travelling exhibits every year. There is one at Stockholm at the moment as I remember correctly. And yes it would be great for them to do something like WB Studio Tour in London and Burbank. People who worked on GoT, for example Tommy Dunne, Deborah Riley, Michael Eaton, Jim Stanes, Gemma Jackson and many others did marvelous job creating all the props, sets, calligraphy work, weapons etc. I would certainly love to see that become a reality.
There are only few choices for that kind of stuff as not many big auction houses do auctions about one film/show. Here are the choices - Profiles in History (they did Hunger Games and Captain America auctions lately), Prop Store (not exactly an auction house but they've been doing show-related auctions for quite a time now; two auctions for Hannibal, Breaking Bad, Dracula), Julien's Live and Screen Used. I don't recall seeing any other auction houses doing auctions centered on one film/show.