To be clear: This is a combination joke / dream question. HBO does not do spinoffs, and GoT doesn't need one. With that out of the way, I feel the marketing oracles would be passing up golden opportunities if they did not consider...:
-- Bronn and Tyrion's Excellent Adventure: A dwarf lord and his sellsword companion tour the Seven Kingdoms, talking to each other and stirring up shit. Potential long-running episodic series. Hijinx ensue.
-- History With Ros: It seems to be thought at GoT HQ that no one's going to watch a scene of worldbuilding or political exposition unless it's spoken to the rhythm of some people getting it on, and Ros has been a primary mechanism for this. In this series which brings her character to the fore, Ros wanders the Seven Kingdoms, having politically and historically educational sex. I'm not sure I'd watch it but it seems to be something the show's into, so why not live it up?
-- Tywin Lannister's Extreme Hunting: Or: "How To Skin a Deer Like A Fucking Boss".
-- The Littlest Murderer: I think GRRM once mentioned ...
vague implicit spoilers
-- All My Walders: This politically and emotionally fraught domestic soap opera focuses on the Twins and the Westerosi misfits who live there.
-- Just So: Prequel series. Syrio Forel. For an hour. Every week. I don't know what lengths I would go to to make this happen.