Union Station has a Food Court. You grab a bite to eat without leaving the building. Download the station's brochure here - http://www.chicagounionstation.com/graphics/UnionStaChi_brochure.pdf .
If you are determined to leave Union Station to eat, then I recommend...
Arturo Express (http://www.arturoexpress.com/aboutus.html at 122 S. Canal St. - basically Canal and Adams St.). They made the best tuna sandwich that I'd ever eaten. Also, you'll really get the Chicago accents and vibe there. They serve fast, quality food at reasonable prices.
Normally, I would recommend Lou Mitchell's, as it is a classic Chicago spot. Yet you have all the luggage and it's really too tight in terms of seating, for the most part. BUT if you want to check it out anyway, see http://www.loumitchellsrestaurant.com/ . It is a few blocks from Union Station though at 565 W Jackson Blvd. I think it's a bit of a trek, particularly since it's cold.
Corner Bakery Cafe (222 South Riverside Plaza, go east -- back of the east outside part of the Union Station, along the Chicago River). It's a chain restaurant. I'm not crazy about it, because the prices are too high, but you can sit down and eat decent food. See http://www.cornerbakerycafe.com .
You can walk across the Chicago River on Adams, then turn right on Wacker Drive. There's a Panera Bread (http://www.panerabread.com ), another chain restaurant similar to the Corner Bakery, at 233 South Wacker Drive. It might a be tight squeeze in terms of standing in line, but I like the place better than the Corner Bakery.
Boston Blackies would be a place to go to get a burger - around the corner from Arturo Express on Monroe & Canal. See http://www.bostonblackies.com/ . I've never eaten there though.
Other than that, you could wait until you get to O'Hare (http://www.flychicago.com/ohare/concessionsohare/OhareFoodBeverages.shtm ), but that's not as much fun.
After eating, go to the Clinton Blue Line train stop to take the L to O'Hare. You'll likely need to go one block west to Clinton (from Canal St./Union Station), then walk a few blocks south (past Van Buren, on Tilden St.) to get to the stop that's under the Congress highway.