1.
Robert Baratheon's Rebellion
Probably the most obvious choice for a Game of Thrones spin-off, portraying Robert Baratheon's rebellion would be a great way to elaborate on the events that are often referenced in the show. It would be a cool way to bring in younger versions of characters we know and also explore some we have only heard of, like Jon Snow's father: Rhaegar Targaryen.
2.
Tales of Dunk and Egg
"Tales of Dunk and Egg" is a series of novellas written by George R.R. Martin about the various adventures of the hedge knight Ser Duncan the Tall, and his squire Aegon Targaryen, who would eventually become the King of Westeros. It could be very interesting to see an adaptation of these characters and the events that lead to Aegon becoming king.
3.
Origin of the White Walkers
Seeing a series set thousands of years before the current timeline of Thrones could potentially be awesome. I'd love to learn more about the Children of the Forest, the more magical side of the lore, and the creation of the wall. Exploring the rise of the White Walkers would almost certainly allow for thrilling television.
4.
Dance of the Dragons
The Dance of Dragons is the civil war between Aegon II and his half-sister Rhaenyra over their father's throne. It is a story that would be filled with the character intrigue and large scale battle sequences we expect from Thrones, as well as a rich expansion of the lore.
So, these are my ideas of what would make the best Game of Thrones spin-offs. Do you agree? What are some of your ideas, perhaps a Lyanna Mormont series? Whatever they decide to do, I think it's safe to say it will be pretty awesome.