If you would really like to experience what it like to rule a great or minor house in Westeros, I highly recommend a Game of Thrones mod for Crusader Kings 2. If you are not familiar with the game, the essentials of Crusader Kings is that you take control of a family in Westeros (Yes, any family) and you play it. You try to acquire land, gain titles, raise a family to be proud of, find suitable marriage arrangements for your family, scheme, plot, war. You do what you want to do essentially.
I can’t say how many hours I’ve put into that game already. I played as John Snow on the wall fighting to restore Winterfell to the Starks. I also played as Dorne before Aegon’s invasion and tried to find a way of assassinating the dragon riders before they came with their armies to burn my home. I played as Stannis Baratheon at the beginning of the Clash of Kings and punished Renly and the rest of the traitors for not bending the knee! This game is simply amazing.
You can purchase Crusader Kings 2 relatively cheaply. It usually goes for under $40 and sometimes as low as $20 on Sales on steam.
The Game of Thrones mod is officially called the “A Song of Ice and Fire for Crusader Kings 2”.