Torcello Island is a small island approximately 5 miles East of Venice. The island's "claim to fame" is a small ancient stone chair which has been nicknamed, "Attila's Throne"-(named after, Attila "The Hun"). Now, the historical evidence suggests that this ancient stone chair was the actual Seat of Power for the Island's Bishop beginning in the mid 500's AD/CE-(and the ancient stone chair may have also been The Seat of Power for the island's earliest Governor). The legend, however, suggests that Attila "The Hun" was actually enthroned on Torcello Island. Does anyone believe that this ancient stone chair on a remote Italian island, was the actual Seat of Power for the Father and King of the Huns?
This Venetian tourist site asserts not:
In reality the Hun [sic] never arrived in Torcello as their descent into North Eastern Italy was halted at Aquileia (UD) and being pastoralist people, they would have never reached an island from the sea.
Aquileia is at the head of the Adriatic, but on the mainland, and closer to Trieste than Venice. Actually, Attilla's next target was Padua, but in 452 Pope Leo I somehow persuaded him to stop.
Recall that the islands in the Veneto were settled by by people fleeing the various Gothic, Hunnic, and Lombard invasions near the end of the Western Roman Empire. Attilla was likely more interested in richer prizes (such as Rome) than pursuing a few soggy refugees into a swamp.
Of the parts of the legend mentioned in your question, one part is probably false while the other is almost certainly false.
Is the stone chair Attila the Hun's throne? As T.E.D. noted in his comment, Wikipedia's page Attila's Throne asserts it isn't. The source for this seems to be this article (which also gives no sources). Wikipedia says the stone is most likely a podesta or bishop's chair.
Was Attila the Hun actually enthroned on Torcello Island? This is almost certainly false as the evidence suggests Attila never visted the island. John Man, in 'Attila the Hun' states that
Aquileia’s surviving inhabitants fled from the Huns to found Venice, which was supposedly a secure haven because the Huns dared not ride their horses into the surrounding mud.
Similarly, Bonnie Harvey in 'Attila the Hun' says
Like Aquileia, Padua suffered great losses under the Huns. Many of Padua’s citizens fled before the approaching army. These 500 people later founded the city of Venice. The Roman historian Cassiodorus reported that “Many families of Aquileia, Padua, and the adjacent towns . . . found a safe, though obscure, refuge in the neighbouring islands [near present-day Venice]. . . .
As these fleeing inhabitants lived to tell the tale, it is fair to assume that Attila was not enthroned in what was their new home.