Discounting the migration across the land bridge from thousands of years ago, did anyone from northeast Asia cross into what is now Alaska and explore North America? I know Russia set up a colony there in the 18th century, but had it between explored before then? Say anytime between 1 AD and the 18th century?
This doesn't quite answer your question, but you may find this interesting. There was a recent article about pre-columbian trade near the Bering Sea. This doesn't mean that this trade extended southward to places like the United States or Mexico, but it does count as contact between the New and Old World.