There's just something about Ned being kind and courteous as expected of him to everyone. Even when it's someone he doesn't like or is opposing he isn't half as cruel as he could be.
The most prominent example I have is how he treats Cersei after finding out about the bastards. He invites her to the Godswood, he touches her face where Robert struck her and politely but firmly gives her the option of leaving. That scene stuck with me because you can feel Cersei softening. I felt myself understanding her more because Ned treated her like a person and held the belief that she was capable of doing the right thing.
It just made me like her a lot more because up till that point all we saw was a stony-faced Queen, Tyrion's japes and children who held hyperspecific views of her that did not align with reality.
The way that Ned interacts with everyone makes you have sympathy for them. Robert especially, the fact that I felt some semblance of empathy even after he hit Cersei and went on and on about killing Dany who mind you, is his second cousin and a literal child, is mostly thanks to Ned and his perspective.
Point is Ned somehow makes even the objectively worst people seem likeable and loveable which is kind of amazing.

















