I believe that the creature having the longest sight range is Glaurung, the first of the Dragons of Morgoth.
Quote:
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But Glaurung lay there, just within the shadow of the great passage that led inward from the ruined Doors, and he had long been aware of the spies, though few other eyes in Middle-earth would have discerned them. But the glance of his fell eyes was keener than that of eagles, and outreached the far sight of the Elves; and indeed he knew also that some remained behind and sat upon the bare top of Amon Ethir.
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- UT, II Narn I Hîn Húrin, The Journey of Morwen and Nienor to Nargothrond
I don't know if this quote is definitive, but eyesight better than eagles & Eves is something special indeed.