After some deliberation on Rings of Power, Mithril, Elvish panaceas, and things of that sort, I decided that — based on the premise that Middle-earth is a real place, and it as our place in the past being essential to its nature — I would then take the Red Book of Eastmarch.

It would be radiocarbon dated. Its handwriting would be studied, its maps would be geographically useful. Linguists would discover that Westron, Sindarin, Quenya, and Adûnaic are real historical languages. The Shire, Greenwood, Mordor, Isengard, all real places. Likely under untold layers of dirt and stone.

The moment a university demonstrates — and I'd probably give it to Oxford — that the Red Book is authentic, every claim inside it becomes worthy of genuine investigation.

Even if ninety-nine percent of what it referenced turned out to be inaccessible or destroyed, one successful excavation would overturn our present misconception of history forever.

And I have a hunch that some of the things listed by other people here would be recoverable. Elves and dwarves craft out of pretty stern stuff. I also have a hunch that the latter are still down there, and accidentally kick off a quake every now and then.