Since this covers a rather broad area and I'm short on time at the moment, I'm going to be relatively sparse on details here. Feel free to ask more specific follow-up questions to get some more specific answers (from me in a couple hours or whoever beats me to them).

At this time, there were extensive maize-farming communities throughout the Eastern Woodlands (basically along the Mississippi River and east to the Atlantic), as far north as maize's growing season allows. Which basically means south of the Great Lakes and part of the St. Lawrence Valley. Southern Florida also didn't rely much on agriculture, as it had bountiful marine resources to support large communities.

West of the Mississippi, the Eastern Woodland agricultural traditions continued up the Arkansas and Red Rivers into the Caddo heartland. Beyond that was a region of non-agricultural communities in the southern Plains, until your reached the Pueblo communities between the upper Rio Grande and the Colorado Rivers.

These regions produced major population centers like Chaco Canyon and Paquime in the west, and Cahokia, Moundville, Etowah, and Anhaica in the east, to name a few.

Any information about the crops these people might have grown or their cultures is welcome.

In addition to maize, squash (including pumpkins) and beans completed the Three Sisters, the dominant crops of this time. Though squash has been grown for thousands of years, maize and beans were relatively new addition to the agricultural suite of the Eastern Woodlands at this time. Once combined, the Three Sisters largely replaced the previous Eastern Agricultural Complex suite of plants. Like squash, a few of these crops continued to be grown though they weren't quite the staples they once were. Most importantly, this includes sunflowers (an honorary fourth Sister). Goosefoot, a relative of quinoa, was still an important crop in the Carolinas at the time of European contact, but had been demoted to a modest household garden vegetable elsewhere. In the southeast, pecan orchards were common. Among the Haudenosaunee (the Iroquois), groundnuts (a root vegetable) were an important cultivated "wild" crop, which I know seems like an oxymoron. The plant was largely propagated in the wild, but was uprooted and transplanted to Iroquoian vegetable gardens. Despite their English name, the "Potato" Clan is actually named after this plant.

Iroquoian use of groundnuts shows us that the line between domesticated and wild plants isn't a sharp one. Many communities managed wild plants to ensure harvests of grapes, lotus seeds, arrowroot, acorns, pawpaws, etc. A broader ethnobotanical understand expands the "crops" of the Eastern Woodlands to dozens of species.

I am totally ignorant about them other than names of tribes that aren't around anymore

Any indigenous nation you can name are probably still around. The ones that have actually been extinguished are poorly known or are actually still around under new names as cultural identities shifted over the last 500 years.

There certainly was Cahokia; roughly 20 000 people living from farming where the Mississippi meets the Missouri. It was at is apogee smack in the middle of your target period, and inhabited by the Mississipian people. These guys grew beans, squash and corn, and apparently also domesticated "topinambours" (Jerusalem artichokes) and a host of other herbaceous plants and tobacco.

Also have to mention de Hurons along the northern shore of Lake Ontario. They numbered about 20 000 in that time period, but lived in smaller scattered farming communities of at most 3500 people each. The Hurons were growers of corn, squash and beans, as well as tobacco and sunflowers . Not sure how many people you require to call a community "large", but there you are...