In Game of Thrones, why didn't Jon take Ghost to Dragonstone?

Because Jon understands the vital lesson that Robb, Sansa, Brann, Rickon and Daenerys do not: beasts need to be free. This is best shown in S3 when Jon joins the Wildlings and Ghost wanders off. read more

Having Jon take Ghost to Dragonstone and show off his white direwolf, an even rarer sight in the north than living dragons, to the Mother of Dragons would have been awesome, but the showrunners likely opted against this due to financial reasons. read more

In season 7 of Game of Thrones, Jon Snow spends a considerable amount of time in Dragonstone mining dragonglass. Dragonglass is known to kill wights and white walkers. Towards the end of "Eastwatch" (Game of Thrones, S07E05), Jon assembles a team of people to bring back a wight to convince Daenerys and Cersei. read more