From what I've noticed most ancient civilizations grew out from the nearest major river system. Be it the Tigris and Euphrates, the yellow river, and of course the nile. This has led to ask why did no native American tribe ever take advantage of the Mississippi River? With it dividing the continent down the middle it seems it could have yielded a major advantage to whoever controlled it.
There were cities and civilizations that sprung up around the Mississippi. The most recent was the Mississippian Peoples whose largest known city is Cahokia. The Mississippian people lived along the Mississippi and their civilization went as far north as Wisconsin and Minnesota, into the southeast into Georgia through Mississippi and out towards the Great plains - they didn't occupy each square inch of each state, they focused on the waterways and river valleys. Their culture did not focus on the woodlands, it was concentrated in the river valleys.
So they did exactly what you assumed they didn't do - they were a collection of tribes that settled in and around river valleys, built villages, towns and cities while engaging in agriculture. Some areas of the Mississippian Civilization also built mounds.
They had a complex and vibrant culture whose disappearance is the subject of debate. The date that Cahokia was abandoned has recently come into question - consensus was 1350 but that has been challenged by fecal deposits and other evidence, see the Berkeley article below, it is possible it was briefly abandoned then they came back and reinhabited the city. When the Spaniards got to Arkansas in 1541 the Mississippians were the first native Americans they encountered. By the time the next Europeans arrive in 1673 their towns has been largely if not entirely abandoned. Their demise was likely a mixture of European diseases and drought.
Sources:
Cahokia https://www.sciencedaily.com/releases/2014/03/140304095029.htm https://www.worldhistory.org/cahokia/ https://news.berkeley.edu/2020/01/27/new-study-debunks-myth-of-cahokias-native-american-lost-civilization/ https://www.history.com/news/native-american-cahokia-chaco-canyon
Mississippian Peoples: https://www.nps.gov/fosm/learn/historyculture/mississippiperiod.htm https://www.nationalgeographic.com/travel/article/spiro-and-the-art-of-the-mississippian-world-in-oklahoma https://www.digitalhistory.uh.edu/active_learning/explorations/1492/1492_cahokia.cfm https://www.uwlax.edu/mvac/pre-european-people/mississippian--oneota-traditions/mississippian-settlements/ http://www.museum.state.il.us/muslink/nat_amer/pre/htmls/m_id.html https://www.britannica.com/topic/Mississippian-culture