Well ok, lets consider the Vikings.
There are reports they landed in America first, so what exactly happened?
http://news.softpedia.com/news/How-Did-Vikings-Discover-America-49891.shtml
If the Vikings had created a small colony there and started to grow a forte, what could have happened then? How would they have likely interacted with the Natives and what kind of cultural exchanges would have taken place. If we consider European dieseases again and the kind of time scale we are talking about would this have given the Native Americans time to adapt to the diseases etc...
Yeah, but the trip from Norway and Denmark to Iceland, from there to Greenland, and on to Vinland was too long. Most European diseases would not last within the crew the whole length of the voyage - they'd burn out before Greenland. Quite a number were also unlikely to end up on the ships in the first place: Malaria was never that far north and Plague wasn't even in Europe yet.
Add to that that the populations in North America were too small to sustain diseases and you've got an interminable problem. Unless you have a large enough population, most diseases will burn through and then be gone. Then your children are in the same position relative to the diseases that you were. Even the initial European colonies in North America were too small by that standard - despite a tendency to be better fed and healthier than their relatives in Europe they consistently had higher rates of die-off when an epidemic moved through. None of them were large enough for a disease to maintain a sustainable presence. It doesn't help that smallpox (for example) went through a hundred years ago, it only helps if it's come through in *your* lifetime.
Now if you're talking about a Viking community staying permanently and inter-marrying with the natives,
they would be slightly different. While they'd still have the disease issue, they might be able to bring something permanent if it was in their livestock. More importantly, they'd be bringing livestock, iron-working, and some crops. The crops wouldn't be much
better than corn, but they would probably include something that could be planted when corn depleted the soil. Which it
always does. Mayan or Mississippian or Olmec collapse, it's only a mystery if you're not paying attention.
So a society with livestock, a more stable crop package, possibly an animal disease reservoir to keep their antibodies paying attention, iron, and maybe even horses could have a few hundred year to spread into either the St Lawrence Valley or New England. Culture wise it would be Norse with a strong flavoring of Iroquois or Algonquin, depending. Genetically it'd be in the area if 2/3 to 3/4 northern European. They'd be much stronger than their neighbors, and have higher population density, so expect them to take the best land (river valleys). Although there would be some transfer of technology and stock to the natives in the process.
When the rest of Europe arrives on the scene, they will be, depending on their start point, either dominating the New England lowlands or extended up the St Lawrence to the Lakes Champlain, Ontario, and Erie. Then, ironically, they'll likely die off more than most Indian tribes. The "best land" - along river valleys - is also where population density and trade routes funnel epidemics. The nearby Indian tribes would be hit less frequently. As populations collapsed, they would come out of the highlands and settle areas the pseudo-Norse had abandoned. [This is essentially what the Cherokee did in OTL, moving from the south Appalachians into better land in Georgia and Alabama as the locals died off.]
The end result would be fairly awesome, but it's still not really what you seem to be looking for.