Well, all the rivers in the central US lead to the Mississippi River, and probably one of the biggest and least known contiguous wilderness area in the US is the area between the levees on the lower-mid Mississippi River, between St Louis and Natchez MS. I don't know the exact dimensions, but the levees are usually 2-10 miles apart and the area is 600 miles long, as the crow flies, or about 800-900 river miles. In some places, such as the mouths of major tributary rivers, the levees are even further apart. Since it is subject to flood, there is very little building or permanent settlement here, and only a limited amount of farming. Most of it is private hunting camps, since fish and game are plentiful throughout the corridor.

Roughly in the middle of that stretch is the mouth of the Arkansas River, where some public land augments the natural flood area, so the wild area becomes very wide as well as very long. Other, smaller rivers also come in near here and centuries of misbehavior by the mouth of the Arkansas have created a maze of channels in the area. That area would be my first choice for a long-term bug-out (I live in Memphis, about 100-150 miles upstream from there).

Other than that, many (perhaps most?) rivers in the US pass through a National Forest, National Wildlife Refuge, or State Wildlife Refuge at some point on their route - there are hundreds of them, covering millions of acres, and all of those are good near term objectives.