The Bedu Hobbits of Far Harad by Anérea

Since it's highly unlikely that Eru plonked Hobbits down alongside the Anduin in Wilderland from the get-go where they hung about unnoticed until the early Third Age, their eventual migration to Eriador probably started in the east. 

Eru knows where Hobbits originally came from, but even if they were among Men who awoke in Hildorien, I imagine the Hobbit ancestors avoided Morgoth's shenanigans simply because that kind of thing is just not in their very down-to-earth nature, and they were quite possibly the first to head (quietly sidle away) west, just to avoid getting stomped on by the larger folk.

By the Second Age they were living a pleasant nomadic lifestyle in the area that later became Harad. But as Númenórean coastal colonies expanded and Haradrim settlements increased, Hobbits would have been increasingly pressed into less hospitable areas. Terrain upheavals and climatic change caused by the rounding of the world would have been a catalyst for them to find a new land to call home. Some may have migrated further south, while others made their way north. With the area around the southern reaches of the Anduin being so populated, their route most likely first went east of Nurn (probably also fairly well populated by this stage thanks to its fertile soils, so not a safe spot for wee folk) then north-west past the gardens of the Entwives (later the Brown Lands), and eventually to the upper Anduin valley. 

I think Hobbit-holes started out of necessity from their desire to remain out of sight, and mind, of big folk, and they developed a nifty technique of half burrowing their tents into dunes to form a kind of disguised fabric-lined hole. 

They've always had good relations with Dwarves and traded with all the eastern clans along their migration, and so had metal and crystal crafted homeware even in their early days. I think they also gained some garden lore from the Entwives, which led to their vegetable growing championships.