Newburn, TN. From there you can take the City Of New Orleans north to Carbondale and Chicago or south to Memphis or New Orleans.
There is free short-term and long-term parking in front of the Lincoln, IL Amtrak station.
Unfortunately, there is no Amtrak train service to Nashville. The old Union Station is now a Wyndham hotel and that is available for viewing. The closest Amtrak station is in Newburn, TN. From there you can take the City Of New Orleans north to Carbondale and Chicago or south to Memphis or New Orleans.
Newbern, TN
28$
No. Amtrak serves neither city.
About eight hours of driving time.
Yes, by the City of New Orleans train.
Along the City of New Orleans, there are stops in Newbern-Dyserburg and Memphis.
"Can you switch to an earlier Amtrak train?"
Amtrak runs a bus service from South Beloit IL to Milwaukee WI. Considering the distance, that's probably as close to "public transport" as you're going to get.
According to Amtrak it is Gainesville, GA (GNS) - about 100 miles from Chattanooga.