Arthur's would probably be mostly positive, because he believes in hanging on to both the good and the bad and after going through so much he's mostly settled into his own skin, so possible sights would be somewhat intangible images of his family alive and happy and together, the lighthouse in Maine where he grew up, Atlantis as it should be all prosperous and whole and busy, the open sea and the dolphin pod he ran with as a teenager (namely his "mother" Porm), etc.

Bucky: if anyone wants to see the more vulnerable side of him, there's always something with his dad and trying to make his dad proud, or his time trying to prove himself in the military. There are also the good points in his life, like off time with the Young Allies and the other Invaders. Anyone wanna see Namor give him his first backhanded compliment?

Renly has delusions of grandeur and is a vain little asshole so his dreaming could be if everything had gone right back home and he'd taken the throne, kept Margaery as his wife, and appointed Loras to his Kingsguard. It would probably be really romanticized and peaceful but also with a veil of sadness because he knows it won't happen. You also might see him in his younger days at Storm's End, playing pretend by himself because he's lonely or doing pretty much everything with Loras over the years.