That's still a point of debate, but scholarly consensus and archaeological data tends to suggest they came from Italy (the peninsula + Sardinia and Sicily), Greece/the Aegean, and Western Anatolia. Their rampage through the eastern Mediterranean was roughly concurrent with migrations of new populations into those same regions.
The "long migration" let me somewhat cautious : they were "Sea Peoples" regionally present before Ramseses III (during Ramses II's reign for instance), and inner european migrations can't explain all movements : Mycenian decline, for instance, isn't that well tied to these (Dorian Invasion being more of a conveinent explanation to fill gaps than really well proven).
Some were known as "settled" peoples, as Lycians (Lukkas) and the identification with places (Shakalusha with Sicily) doesn't sounds that definitive to me : it could be as well tied with other places (Skakalusha with Salawassa/Sagalassos in western Anatolia)
Eventually, I'm more convinced by a Adriatic/Agean/Anatolian origin than an Italic one, at least for what matter to the bulk of Sea Peoples. That said, as you mentioned, the debate is far from being closed.
BTW, what's your opinion on "1177 B.C.: The Year Civilization Collapsed "? It just got translated there, so I bought it and it was definitely interesting and (that's the trick) more tied up to the question at hand : on non-migrating factors and focus on peoples such as Gasgas that aren't "usual suspects" when it come to the fall of Hittites as generally introduced.
But while it's interesting, when it come to having an holistic view of the eastern basin, it looks a bit "catastrophist" for me, as in focusing a bit too much on ecological factors (now, he's hardly the only one, and this precise point of view isn't bad in itself, but it's quite the historiographical trend now, and found among really diverse studies on other periods).