Departure of the Galadhrim

[Inziladun]

Originally Posted by Eönwë

So where did they go?

I don't recall anything to say definitively where the Lórien Elves went, but I think Mirkwood would have been the most likely destination. It was geographically near to Lórien, and its people would have spoken the Silvan language the Lórien Elves knew.
I can't see them going Over Sea, at least not at once. The sea-longing had to be awakened in the Silvan Elves before it would manifest. Before Legolas journeyed by the coast, he never had any desire to sail or be near the Sea.