Riding Amtrak trains from NYC to LA you can expect to see a just about every kind of scenery the US has to offer.
You'll also be able to contrast the air travel hustle, bustle, crowds, and treatment as a suspected terrorist with the much slower pace and dignified experience of US train travel.
If you're used to travel on UK and European trains you may find US trains not quite as spiffy. The US government is quite stingy with funding for Amtrak and
Amtrak's rolling stock is some 40 years old now.
You have a number of train route options for getting from NYC to Chicago:
1. You could take any train out of NYC that will get you to Washington DC in time to catch the
Capitol Limited @ 4:05 PM. The CL would give you 6 hours or so to sight see in downtown Chicago before the Southwest Chief (SWC) departs.
2.
Lake Shore Limited - The LSL would give you about 5 hours to sight see in downtown Chicago.
3.
Cardinal - Hoosier State - Again, you would have about 5 hours to sight see in downtown Chicago. Many think the Cardinal is more scenic than the CL, LSL with the LSL being #2 of the 3.
The Cardinal uses
single level cars and only runs 3 days a week - Sunday, Wednesday, and Friday from NYC.
September is towards the end of the summer travel high season.
The trains may be carrying a lot of passengers when you travel.
You don't say if you will be in coach or if you will have a sleeper berth.
Either way, the CL, and the SWC have a Sightseer Lounge car (SSL) that makes sight seeing very easy.