I would like to learn more about the Pre-Columbian history of native peoples who lived east of the Mississippi River, especially anything known about their political history, written languages, trade routes, major trails/roads, major wars, treaties, famous leaders, towns/cities, etc. What book would you recommend that covers these topics in a readable way?
I like to recommend George Milner's The Moundbuilders: Ancient Peoples of Eastern North America as an introductory text. It covers a broad enough selection of time and space to give you a good overview of the region and its major archaeological cultures without getting bogged down in the details. The Handbook of North American Indians, vol. 14: The Southeast and vol. 15: the Northeast are good resources to look into as well if you have access to a copy. They're mainly focused on historic nations, but the also have chapters on Precolumbian archaeological cultures too.
With the big regions out of the way, I'll hit a few of the smaller ones too, with an emphasis on accessibility.
Ohio Archaeology: An Illustrated Chronicle of Ohio's Ancient American Indian Culture
Cahokia: Ancient America's Great City on the Mississippi
Before and After Jamestown: Virginia's Powhatans and their Predecessors
The Timucua and The Iroquois, both part of The Peoples of the America series which might have some other books you'd find interesting, are mainly concerned with the historic period of their respective cultures. But they both begin with a chapter or two on the Precolumbian archaeology of their regions. One caveat I'll mention here is that Dean Snow favors a late date (mid-1400s) for the founding of the Haudenosaunee (the Iroquois confederacy) and has been critical of more recent studies that indicate a founding date in 1142 CE. That's a debate we can get into at another time, however.
While not part of The Peoples of America series, Huron-Wendat: The Heritage of the Circle follows a similar pattern, with a chapters on traditional Wendat oral traditions and modern archaeology preceding chapters on historic Wendat culture.
Knights of Spain, Warriors of the Sun: Hernando de Soto and the South's Ancient Chiefdoms is a bit heftier than most of the books I've mentioned here so far, but it covers the Southeast Mississippians very well. Using de Soto's entrada as its frame narrative, it periodically detours from its summation of the historical events of the late 1530s into the early 1540s to explore the deeper archaeological context of each polity de Soto encountered.
Also moving a bit further away from the Precolumbian, there's Indian New England Before the Mayflower. As its name suggests, it's not really Precolumbian, but pre-Mayflower. It does, however, do a great job of covering daily life in the region in the late 1500s / early 1600s, before Europeans began showing up in large numbers. Along a similar vein, The Powhatan Indians of Virginia: Their Traditional Culture does the same for the Virginia region, but it'll largely be an elaboration on material you already covered in Before and After Jamestown.
Finally, if you want information on the trails, there's Indian Trails of the Southeast, Ohio Indian Trails, and Paths of Pennsylvania (that last one is a pdf link).
I could probably go on for a while, but that should be enough to get you started. If you have any specific questions, feel free to ask them here.