Well, what motivates exploration and discovery?
The quest for expansion of territory...yes but it seems most of the empire-building colonial expansion involved travelling south and east from Western Europe. The idea seems largely to have been that there were many known, settled lands which could be taken over and exploited by our ancestors, and indeed they spent many centuries pursuing their dreams in this way without necessity of the long and highly uncertain crossing of the western ocean.
The quest for unoccupied land, or available land for farming, by an ever-increasing population that was running out of farmland in realtion to the population (and the law of primogeniture meant that the firstborn son got the family land, the rest had to look elsewhere). Trouble is, until there was enough known about prospects in North America that official sponsored emigrations were organized, those without resources in their native countries wouldn't generally have had the resources to mount a trans-Atlantic voyage.
History has allowed for the occasional independent wanderer--St Brendan being the best known.
However, consider the merchant class which dealt in finding goods abroad and shipping them back to Europe. Of course they would have both the motivation and the means to come to eastern North America, if they thought there was a profit in it. And the stuff they wanted was here: whales, cod, walrus, and lots and lots of timber.
It is entirely credible that they would have set up expeditions to Newfoundland, Labrador and possibly farther inland. BUT NOT TOLD THE WHOLE WORLD WHERE THEY WERE GETTING THEIR GOODS for obvious reasons. They didn't want the competition here. Logically they might have set up at least seasonal, and possibly semi-permanent settlements to organize their resource-harvesting activities.
The Greenland route to North America has some obvious inconveniences, but can be accomplished in relatively short hops rather than by direct trans-atlantic voyaging. Since these would have been commercial voyages, their objective would have been accomplished once they had a shipload of stuff...no need to continue exploring the unknown continent.
And maybe I'm nuts, but it also seems logical that the most successful merchant traders would have been the ones who established a useful working relationship with the native peoples who were here already and knew where the fish were. It's a matter of historical record that this is why the Vikings failed in their Newfoundland efforts--peaceful coexistence was not in their nature, but they were severely outnumbered by the natives, and eventually just gave up.