Now you might think of Iceland and Norse Greenland as a counter example. But Norse Greenland never really thrived, and was eventually abandoned. Iceland however thrived, but it is so much closer to Norway about 7 days at see with the potential to stop at the Faeroe Islands.
The voyage between Greenland and Iceland is similar (only a bit longer + sailing up the west coast of Greenland). And finally you need another week or two to cross the Labrador sea from Greenland. However that route is much harder in the winter then between Iceland and Norway, and Greenland is not nearly as populated as Iceland or Norway and don’t generate enough surplus food which they can supply to a potential colonies on the North American mainland.
So the logistics of supplying a colony in North America without help from the people already living there must include a summertime only supply line from Iceland with enough supplies to last the whole year. Where each voyage from Iceland is going take maybe a month, maybe more, just one way. These ships are still pretty small and not a lot of room for cargo, so you’ll need a few of them. I’m not sure the economy on Iceland could have afforded such an expensive endeavor.
There seems to be a need for a minimum primary settler population and a decent amount of native assistance- it's fairly easy to build a new town 10 miles from your last but I am not aware of any long distance unsupported settlers.
So if the natives around the Mayflower had all died, so would the Founding Fathers. If the Norse diseases had killed off the locals they might not have made it through winter.
The Narragansetts were the most powerful tribe in the southern area of the region when the English colonists arrived in 1620, and they had not been affected by the epidemics. Chief Massasoit of the Wampanoags to the east allied with the colonists at Plymouth Colony as a way to protect the Wampanoags from Narragansett attacks. In the fall of 1621, the Narragansetts sent a sheaf of arrows wrapped in a snakeskin to Plymouth Colony as a threatening challenge, but Plymouth governor William Bradford sent the snakeskin back filled with gunpowder and bullets. The Narragansetts understood the message and did not attack them.
There were 18 years between the European settlement of Pitcairn island and the next visitors - https://en.wikipedia.org/wiki/Pitcairn_Islands#European_sett... .
Your constraints are pretty strict. There aren't many places which could be settled (in recorded history) where there weren't already people living there, and where there was a reason for not continuing contact with the place of origin.
Another possibility is Te Pito O Te Kainga / Rapa Nui / Easter Island. The first explorers met one person already there (Nga Tavake), then they go back to Hiva, and a double canoe returns to Easter Island carrying the settlers. They left "because a rising tide was destroying their land" and/or a power struggle with the Hanau Eepe, if I read http://archive.hokulea.com/rapanui/hotu.html correctly. In either case, the oral history suggest little continued connection with Hiva.
Hunting and fishing shouldn't be very different in Newfoundland compared to Norway/Iceland. Bring a few chickens along, and you have another food source.
I assume/guess the vikings were better at this stuff than the Mayflower crowd.
Not least of all, Leif Eriksson was a Christian, a Catholic in modern terms. It's reasonable to assume most of his followers were, too. He had gained the epithet "the lucky" due to his habit of coming across and rescuing castaways at sea. To the Norse, luck was evidence the cosmos was on your side, and one of the most important attributes a leader offered to potential followers was a share in this cosmic luck. This probably helped Leif the missionary securing a lot of conversions!
But the heart of Christianity at the time was in Rome. They were already profoundly cut off from the mystical fellowship of believers, the communion. How much worse wouldn't it be for their sense of self if they were not only to go off in an impossibly distant land, but to live as the savages there?
Reality is more complex and challenging than Farmville or AnimalCrossing.
The settlements in Greenland never really reached that point. The leading hypothesis at this point for why Greenland collapsed was that the Arctic trade routes dropped far-off Greenland from their destinations--and without that trade, the settlements couldn't sustain themselves and collapsed. Newfoundland may be a more hospitable place than Greenland, but from a trade situation, it's even worse: it's not offering any trade goods to Europeans that Greenland or Iceland could be providing (at much shorter journeys), but it's still probably not able to tap into the North American trade network--I think you have to make it to Nova Scotia or New Brunswick to do that.
Ten generations is completely sustainable by my standards.
https://en.wikipedia.org/wiki/History_of_Greenland#Norse_set...
And of course the Greenland colony wasn't really sustainable, which is why it died out when a couple of hard turns came their way (climate change and getting cut off from trade for a few years).
Surviving winter solo or in a small group is damned near impossible.
But then again farming populations can expand really fast with low population pressure. The 13 colonies were seeing their populations double every generation just from natural fertility even before immigration.
For settling uninhabited locales you've got Shetland, Mann, the Isles, Iceland and some seasonal settlements on Greenland.
You might also check out the podcast History of Byzantium. Although you'll have to go many hours before encountering the Norse, in the form of the Varangians.
And I also recommend the excellent book Children of Ash and Elm for a very recent overview of Viking history.
It's not much, but it's a start.
Are you calling Normandy one settlement? As they certainly spent most of the Viking age colonizing from Iceland to Sicily.
Viking was a lifestyle or temporary occupation, not a people. The people were the Norse, and they did a massive amount of settling in the Viking Age.
Of course, if the native population died off around them, the Vikings would probably have expanded their settlements and perhaps ruled North America instead.