Aragorn
He is much older than you would assume by his appearance, and has seen a lot. There's a lot of backstory to him, which would very nicely compliment the LOTR movies and give more context to his relationship with other characters.
There could be an episode either as the prologue or a recollection about how his father gets killed and he is sent to Rivendell.
His relationship with Arwen, how they meet and how they fall in love with each other.
His relationship with Elrond, who was a father-figure and a mentor to him. Imagine we could see him grow up without any burdens of his heritage, and then later learn from Elrond who he truly is, how he gets the Ring of Barahir and the Shards of Narsil.
How he meets Gandalf and gets trusted with guarding the Shire.
We could see beloved locations from Lothlorien to Rohan as we follow Aragorn on his journey. He was a great adventurer, and this could also be a way to give the creators a free imagination to a certain degree, and create new adventures and new characters, which were not in the books, but could fit there. I'm usually not an advocate for such stuff, but there could be new characters created who do fit in greatly with the storyline without causing any harm to known events and characters. Like orc raiders or a long forgotten tribe of Rohan doing their own thing out in the wilds. What of the general population of Rivendell and Lothlorien? Elves we never encountered in the books or movies, but would be important in the early years of that human child growing up amongst elves.
The conflict between Elrond and Arwen, when he finds out that his daughter would choose love and death instead of the eternal life she was born with.
Another scene which was mentioned in the LOTR movies would be Aragorn chasing Gollum to gather information about the One Ring. This could be extended and explained a lot more, we could journey into Moria again.
And it could end with Aragorn walking into the Prancing Pony in Bree and taking his seat from where he's watching the hobbits arriving.
But... maybe there could be a second season of his life with Arwen after the events of LOTR.
And yes, I would only accept this is Viggo Mortensen would play Aragorn again because there's no one else who could do it better. Same goes for the other well-known characters as well, so we better get this approved and start shooting while Sir Ian is still gracing this world with his presence.