I'm reading a bit about how many different groups could possibly have visited the New World before Columbus (the Vikings, Indonesia, Japan, etc) with varying levels of quality of evidence to back those possibilities up. It's odd that I don't see much discussion of the possibility that someone from the New World visited elsewhere. Did anyone from the New World ever visit Europe or Africa or Asia or Oceania?
Genetic evidence suggests three possible pre-Columbian journeys from the Americas to other parts of the world. The presence of haplogroup C1a in southern Siberia is possibly due to a back-migration across the Bering Strait (Dulik et al 2012) but the time-depths involved here muddles the picture. Genetics studies of the Rapanui from Easter Island indicates Pre-Columbian admixture with Native Americans (Moreno-Mayar et al 2014), likely as part of the brief Andean-Polynesian exchange mentioned in another post linked here. Haplogroup C1 has also been present in Iceland for at least 300 years, possibly going all the back to the days of the Vinland expeditions 1000 years ago (Ebenesersdóttir et al 2010. Of course, changes are in this case that the Native people who went to Iceland did not do so voluntarily.
Getting into oral traditions, there are a few other examples. I talk about two of those in this post: Did Native Americans have any folk stories / tales of pre-Columbian explorers? Keep in mind that it's challenging to separate legend from history here.
There's always room for discussion, but perhaps the section Pre-Columbian Trade and Contact from our FAQ will answer your inquiry.