As someone who has gone to CHI frequently the last month or so, I figured I'd chime in. For one thing, they do have lockers where you can store your bags (so you don't have to drag them around all day). You do have to pay, though - however, you can always just check some bags if you're not going to need them until getting to your destination. There's definitely a lot you can do in Chicago during that time - you could go to either a Sox or Cubs game (depending on which teams are home), go to some of the museums, go to the lake or one of the parks (Millennium Park or Grant Park), or go to the Magnificent Mile, just to name a few ideas. The Willis (Sears) Tower Skydeck and the John Hancock Observatory are also a great way to see the city - though make sure there is visibility on top before paying the admission charge! You could also go to the Lounge at the top of the John Hancock building for drinks - definitely expensive, but you don't have to pay for admission to the Observatory and get the same view!
If you decide you may want to go anywhere beyond walking distance of Union Station, getting a CTA daily pass would be a good idea - the buses/trains run frequently, and you can get around for a fraction of the price of a cab. Unfortuately, they don't sell the 1 day pass at Union Station, so you'll have to go to the nearest store which sells them - CVS is one (there is a comprehensive list on the CTA website). This will let you use all the L lines and buses - to find routes, Google Maps is quite helpful. Nearest L stations to Union Station are Clinton (blue line), Quincy/Wells (brown, orange, and pink), as well as Jackson (red - a bit farther than the others, though...). There are also others within walking distance, and there are stations where you can transfer between lines - once again, Google is your friend here. If you want to stick with cabs, there's plenty of them in Chicago as well - just hail one if you need a ride. Some of them are notoriously resistant to accepting credit cards (even though the City requires most cabs to do so), so it may be a good idea to keep cash on hand.