Tolkien was enamored of the tale of St. Brendan, which is wrapped up in the Hy Brasil myth, as davem points out.
There is also Tolkien's Atlantis "nightmare", dream, what have you - the green wave - from which derives his Numenor mythology.
Both these legends have to do with western seas.
It is interesting to me that the one exception (in the First Age) is the coming of the Noldor, Eastwards, out of the West. The Numenoreans are the second instance (though not an exception, having arrived from the West to establish empire in the 2nd age, not the 1st).
Historically, the oldest civilizations are in the Far East. Population growth has been enormous there compared to the west (such as Europe) for thousands of years. Since before the Roman Empire, there has been pressure on barbaric tribes to push westwards. Why Europe never developed Empire until after the medieval era, may have much to do with the land being good and the people being relatively stable (if not content) with their lot.
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