Before I go around making all kinds of setting changes to Middle-earth to make it more conducive to a sword & sorcery pulp feel, let's explore some of the potential eras in which I could set a game. All of these are in the Third Age of Middle Earth, but far removed from the War of the Ring itself. There's plenty of years to play around with here; the Third Age lasted for over 3,000 years, and started at the Fall of Gil-Galad, Elendil and Sauron himself, and ended with the end of the War of the Ring after the end of Return of the King. For context, that's nearly as long as the period of time between the Trojan War and now; although the longer lives of characters in Middle-earth tends to extend the years somewhat, I suppose.
1) In the 1060s, the reign of Gondor's Ship-kings has just come to an end. Gondor is at it's apex, having conquered much of Near Harad, controlled South Gondor (or Harondor) and Umbar. Political upheaval of the southlands. Arnor is already divided, although all three kingdoms remain strong(ish) yet at this point. The Istari are only relatively recently arrived and not yet famous. The first hobbits reach Eriador. Although the Northmen of Rhovanion are not yet allied overtly with Gondor, they are still on relatively friendly terms. Greenwood the Great starts at this time to get its shadow and is starting to become called Mirkwood.
In this era, most likely a game would focus on political intrigue in the Southlands. Sauron is quiet, as are his direct servants. The distant echoes of problems in Greenwood would barely reach the ears of the kings of Arthedain or Gondor either one. Arnor is broken and provincial, while Gondor is at the height of its power.
2) In the 1250s, on the other hand, Gondor is fighting (or just fought) a large horde of Easterlings, and ties with Rhovanion are established. By this time, Mirkwood is known (at least by the White Council) to be occupied by what is thought to be a Nazgûl. Lands to the east as far as Dorwinion and the Sea of Rhûn could all feature here. In the north, Arhedain remains strong, although the Dunedain of Rhudaur have failed and the country is occupied by Hill-men. Cardolan also has a waning nobility. Until the founding of Angmar in fifty more years, however, Eriador is fairly quiet and peaceful, other than squabbles over borders (and Palantiri) between the three north kingdoms.
3) By 1410, Rhudaur is completely conquered and overthrown by Angmar; if a kingdom by that name even still exists, it is a puppet kingdom of hostile aliens, friendly to Angmar. Cardolan is ravaged, but survives, as some survivors of its citizens flee in the the downs or the Old Forest. The King of Arthedain is slain and Amon Sûl (the tower on Weathertop) is destroyed. Despite this, later in the year, the northern Dunedain, with help from their allies from Lindon, Rivendell and even Lothlorien manage to beat back the assaults and pacify (for a time) the border with Angmar.
4) A few years later (1432), the disastrous, fifteen year long civil war called the Kin-strife in Gondor takes place. The rightful king is overthrown by Castamir the Usurper. Osgiliath is burned (although not fully depopulated, and the king flees to his mother's kin in Rhovanion for a decade. When he returns and overthrows the Usurper in 1447, it is a bitter affair, and the rebels hold out under siege at Pelargir for a full year, before they decamped and took the entire province of Umbar with them as a rival power, supported not only by these dissidents, but also Black Numenoreans who still lived in the area.
5) By the 1850s, Araval, king of Arthedain, has been at war for 400 years with Angmar. Cardolan is desolated, and now populated by the Barrow-wights; Rhudaur is now the Coldfells or Ettenmoors and the Trollshaws because of their hostile inhabitants, although some villages of rangers remained in the Angle. Arthedain will hold out for nearly a hundred and twenty five more years, but the sad defeat and decline is a prominent theme here, as well as constant wariness and low-grade warfare. In Gondor, the disastrous invasion of the Wainriders truncates Gondor's eastern frontier, and the king is killed, and Gondor's allies, the Northmen of Rhovanion are enslaved, although some move to the Vales of Anduin and become the Éothéod. The Wainriders will not truly be defeated for fifty more years, and much suffering in both Gondor and among the Northmen still lies before them.
You may notice that these proposals focus considerably more on the Men of Middle-earth than the elves, or dwarves, or even the hobbits. Yep. I haven't decided what, exactly, I'm going to do about elves and dwarves, honestly—probably replace them with something a bit less mythic and more pseudo-scientific. Or maybe I'll just minimize their importance even more than it already is.
The Dunedain I will treat much like later Romans; a great and grand civilization; the greatest in the world, at this point, but politically fractured and in decline. The Northmen are like various Germanic tribes; some of the common men of Eriador and Gondor are like pacified Gauls or other Celtic groups, and the Wainriders and Easterlings are like the Scythians.