Railfan! Blue Island, Colton Jct. etc.
West Chicago also offers a railfanning opportunity, since a north/south rail line(the former Elgin Joliet and Eastern/EJE, I forget which freight railroad bought EJE out) intersects with that Metra line. Also you can walk right onto the former Joliet Union Station platform if you take the Rock Island Metra to Joliet, and can see all the freight train action going through that junction up close. There is now a railing on the north/south(ex-Amtrak) and east/west(ex-Metra) platforms, as of today.
Are you interested in maximizing rail time, and/or interesting rail experiences, or are you looking for an easily reachable there-and-back trip where the destination itself is interesting?
In the latter case, you can easily head up to Milwaukee and back on the Amtrak Hiawathas, and there's plenty to see and do there...though arguably much less so than in Chicago. There are a few Chicago suburbs that are neat to explore and easily reachable by frequent METRA service, such as Geneva, Kenosha, Naperville and many others.
If you want a "different" sort of rail experience, the electrified South Shore Line to South Bend and back is a good one, though there's nothing particular to do in South Bend while you're there, given the station's location.
If you just want to spend the day on Amtrak, most of the Chicago-based corridor services have schedules that allow out-and-back day trips, including to St. Louis, Detroit, Carbondale and Quincy...but you wound't have much time to do anything meaningful at those destinations.
Just a note if you do Kenosha: the train service on that line north of Waukegan, is MUCH less frequent. I strongly recommend doing a trip on Monday-Saturday, and not to do one on Sunday or holidays. There also is local bus route service within that town, but the service is much better on weekdays vs. Saturday. On Saturdays, all the routes that run on Saturday(less service vs. weekdays, sadly) end by like roughly 4pm.
You can use Uber or a cab, if you need to get somewhere within that town. I want to say Lyft may now be available in Kenosha, but not 100% sure on that.
I'd also suggest Milwaukee (perhaps not surprisingly) as an easy day trip with more Amtrak train options than any of the other Chicago corridors - you'd have up to about 11-12 hours in Milwaukee.
And I'd also agree with South Bend (via the South Shore line commuter train), primarily for the street-running in Michigan City as the South Bend station is at the South Bend Airport and not particularly exciting - although it is possible to travel onward to downtown South Bend and other points in the South Bend area via local transit.
St. Louis is another option, as well as any of the other cities along the St. Louis route (such as Springfield) - you'd have up to 5 hours in St. Louis.
For South Bend, you'd transfer to the #4 Transpo bus at the airport, to get to downtown South Bend. That bus route picks you up(and drops you off) on the access road, immediately south of the South Bend Airport station. It does have some limited things to do, but I wish SB had more things to do. Michigan City seems to be trying to make their downtown nicer, based on recent trips I've done there. It even now has 2 breweries, that are within walking distance of the downtown Mich City South Shore stop. And of course, Saint Louis is really great and has a lot of stuff to do. You can take Metrolink(light rail) to get to various parts of that city, and there's a stop just outside of the Amtrak station in Saint Louis.
I agree with the recommendations for Galesburg,the Henry Ford Museum and the SouthShore Line to SouthBend Eddie!
Also consider a trip to the Historic Pullman Village and the Illinois Rail Museum although a car or ride share is necessary for these two.
Galesburg is alright. It does have the birthplace home of Carl Sandburg, Knox College's campus, and a few shops downtown like a bookstore. And of course like you said, it is good for railfanning. I feel bad for that town since years ago the Maytag plant there closed, and a lot of jobs were lost.
I will add that if you go to the Pullman neighborhood of Chicago, you do NOT need a car to go there. You just only need to take the Metra Electric line, to the 115th/Kensington stop. Unfortunately for the Illinois Railway Museum, you would need to rent a car to go there. It'd be nice if they provided a shuttle from like the Crystal Lake or Woodstock Metra stop, but sadly they don't. I've heard some people take a bike on Metra to Crystal Lake(or Woodstock, whatever they prefer), and bike over country roads to IRM though.