Maize originated in southern Mexico. This is where the earliest archaeological evidence of maize is found, as well as maize's nearest wild relative, teosinte. It first makes its way into what's now the United States about 2,100 years ago, moving from Mesoamerica into the American Southwest. Between 2000 and 1600 years ago, during the time of the Hopewell - a huge complex of cultures that traded over vast distances and engaged in similar religious practices - maize made its way eastward into the Mississippi Valley and beyond. But at this time, its still a rarity. Only a handful of cobs have been dated to this time period in the region and the likely were an exotic import from distance lands rather than something grown locally. Around 1400 years ago, in the lull between the Hopewell and the Mississippians, the people in the Middle Mississippi valley (around St. Louis) either develop or import a variety of maize that can be grown locally in abundance, transforming it into their staple crop. By 1000 years ago, maize-based agriculture had spread over most of the Eastern Woodlands and displaced many of the old crops that had been part of the Eastern Agricultural Complex (a suite of crops that had been grown in the area for millennia before maize arrived; sunflowers and some types of squashes are the most famous members of this group). Maize was later followed by beans and non-native squashes like pumpkins. However, even by the time Europeans arrived in the Americas, maize was rare in the upper Mississippi Valley; the climate wasn't particularly favorable and wild rice was readily available, making maize-based agriculture hardly worth the investment of time and labor. Along the Missouri however, maize-based agriculture extend even to its northern limits and the societies farming the narrow corridor where maize could get enough water to grow did good business trading with neighboring Plains cultures that couldn't grow it themselves.

In a similar fashion, tobacco also moved from south to north. It did so a bit earlier, reaching the Eastern Woodlands sometime around 2100 - 1800 years ago. And it came from much further south, being native to the eastern slopes of the Andes. Unlike maize, it doesn't seem to have passed through the American Southwest first but came directly up the Gulf coast, since a different species of tobacco (also imported from the south) dominates the Southwest.

Those are the main, widespread examples of non-native plants being transported and grown in the Pre-Columbian Eastern Woodlands. There are other examples of landscape alternation in the area, but I don't think they really fall into your trade focus here.