printman2000 said:
You may have time to go to the Museum of Science and Industry. You can take a Metra train from Union Station. Looks to be a great museum. I hope I have time to get to it in July.
http://www.msichicago.org/
Actually, one can't take Metra from Union Station to the MSI. The closest Metra stop to the museum is (I think) 55th/56th/57th, which runs out of Randolph/Millennium Station near the lakefront. Union Station is about a mile or so west of there.
As for connecting between the Capitol Limited and the Texas Eagle, it depends on how close to on-time your arriving train is. With the Eagle leaving at 3:20, I'd be back at Union Station no later than 2:30 pm.
Now, if you're interested in "sightseeing" sightseeing, others have given suggestions on what you can do. It really depends on what you're interested in. If you're interested in railfan sightseeing and riding some of the transit lines, I'd recommend a ride on the Brown Line (Ravenswood), which runs from the Loop, northwest to Kimball/Lawrence and back. The ride is nice, and towards the end, you're literally in the middle of an alley, with the tracks passing by people's garages. You get a similar effect if you happen to be on the line to 54/Cermak, but you have to exit the fare-paid area and re-enter (costs 25 cents for a transfer on your transit card, or an extra fare if you happen to lose your card).
If you ride the Brown Line, allow for about an hour and a half for the round-trip (it shouldn't take quite that long, but just to be on the safe side).
Riding the Orange Line to Midway is also interesting, but (in my opinion) the Brown Line is more interesting, at least from the standpoint of the transit operation (the Orange Line parallels a busy freight line, but other than that its route isn't anything special).
If your trip happens to be after the end of June, you can ride the new Pink Line, which replaces the Blue Line to 54/Cermak, operating through the loop elevated instead of the subway.
If you're interested in riding older equipment, then ride the Blue Line (or the Pink Line when it starts running), as that/those line(s) run the 2200-series cars, built by Budd way back when. They are identifiable as being boxy-looking and have double-sets of doors, as opposed to the wide sliding doors on the rest of the cars. In reality, though, all CTA cars are pretty much the same, with just some minor differences between the different series.
As I noted earlier, to get to the Loop, exit Union Station and walk east across the river, and about two blocks to Wells Street (you can't miss it).
Probably stuff I'm forgetting, but I'm tired. Any more questions, feel free to ask.