The Wilderness of eastern Eriador (somewhat conjectural)¹

At the end of the Third Age, the lands between the Bree-land and the Misty Mountains had become wild and pathless. The old East Road still ran through these lands, a remnant of more civilised times, but away from the road a traveller could easily become lost in the untamed wilds. Thus, when Elrond heard from the Rangers that Frodo and his companions had set out from Bag End, and that they were pursued by Black Riders, he sent out his allies into the Wilderness to search for them and give them aid. Aragorn was among these, and travelling along the East Road he found the Hobbits and gave them his help in the rest of their dangerous journey to Rivendell.

It is difficult to be sure whether the 'Wilderness' between Bree and Rivendell was a named area in its own right. In most cases, it's simply referred to as an (uncapitalised) 'wilderness'. On one occasion, however, Glorfindel speaks of the (capitalised) 'Wilderness' as if it is the name of the region, perhaps roughly equivalent to the 'Lone-lands', rather than just a description. In either case, the 'Wilderness' west of the Misty Mountains is not to be confused with the 'Wilderland' of Rhovanion, which lay beyond the Mountains to the east.