You could eat at Giordano's if you call ahead. The deep dish takes 45 minutes to cook.
The Art Institute isn't worth it if you can't spend a whole day there. It's HUGE. We spent a few hours there and barely saw two wings.
Navy Pier has a lot of shops and restaurants, along with the Ferris Wheel and swings (I don't recommend either in January, though). It also has an excellent Shakespeare theatre. You won't have time for a show, but you could browse the gift shop if either of you are a fan. The restaurants include Harry Caray's Tavern, Billy Goat Tavern (famous from the SNL skit with John Belushi -- "Cheeseborger, cheeseborger! No fries! Cheeps! No Pepsi! Coke!"), Haagen-Dazs, Bubba Gump Shrimp, Jimmy Buffett's Margaritaville, and a food court that features the famous Garrett's Popcorn (be sure to pick some up for the train).
They offer discounts to members of the military:
http://www.navypier....n_shop/uso.html
http://www.navypier.com/ for a list of stuff.
The #124 Navy Pier Express bus will pick you up from Union Station. You could also take a cab, since it's not very far... I'd say a $10 fare at most.