[Zigûr]

I would argue that Professor Tolkien never intended to flesh out the details of the geography of Rhûn and Harad or the history and societies of the Easterlings and Haradrim for two reasons:

1) These locations were almost permanently under the Shadow, and information about them was not common knowledge in the West, so it would be inconsistent to have the fictional "authors" of the stories to know about them. We can hazard a guess at how they might have appeared judging by the sketched world-maps in The Shaping of Middle-earth but it's hardly definitive. Saruman had been in the East and Aragorn to both the East and South, and I would hazard a guess that some information might have existed among the scholars of the Dúnedain, but nothing well-known or indeed especially relevant to the major tales of Middle-earth. In Letter 131 Professor Tolkien writes that "the North-West is the only part clearly envisaged in these tales."

2) Leaving the details vague contributed to a sense of mystery which Professor Tolkien found appealing; see Letter 247 where he worries about publishing The Silmarillion because exploring the backstory of The Lord of the Rings might "destroy the magic, unless new unattainable vistas are again revealed." I think confining the details to the North-west is important for the same reason.

I don't think there really was anything important further North in Middle-earth, incidentally. I've often wondered if things like the use of chariots by the Easterlings (a feature of ancient Middle-eastern warfare) and elephant cavalry by the Haradrim (used by a variety of ancient cultures) was meant to reflect significantly on their relationship with the more early-medieval flavour of Gondor, Rohan and the like.