The river

The sea took the raft and tossed it about as Autumn winds whirl thistledown round and round upon a road. (It was as though the South, North, East, and West winds were all at once tossing it back and forth.)

Thank you, Homer, for specifiying what kind of winds, it affirms my assumption it must have been autumn and if we add the 17 days at sea to the starting date of November 22nd, the date by now must be the 9th of December. As a result of Poseidon's fit of rage Odysseus is swept off his raft, floats in the sea for three days and nearly drowns. It's only with the help of Athena that he manages to survive by swimming up a river:

After 17 days of sailing Odysseus has almost reached Scheria on his raft, when the God Poseidon unleashes his anger at Odysseus leaving Ogygia by furiously stirring his trident to generate violent winds and waves.

And then he swam, he came to the mouth of a beauifully flowing river. That seemed to him the best place, smooth of stones and also there was shelter from the wind.

The river pictured on the left is close to the city where the Phaeacian king Alkinoös and his daughter Nausikaä lived. The name Nausikaä is why I think this must be the river where Odysseus came on shore. Please note the tiny island in the red circle.

Odussey Book 5 line 313-332 Samuel Butler
Odyssey Book 5 line 404-407 Barry B Powell