How many people are in the group? If you have several, you may not all fit in a standard taxi and may need a van; in that case, get a phone number so that you can call when the train pulls in.
Do you have your tickets to the Harry Potter exhibit already? The tickets are timed, and weekend demand is very high. Be careful about how late your train may be; if you miss your ticket time you may have a bit of a problem on your hands. (If you don't have the tickets now, go to
www.msichicago.org and follow the directions to order them.) Also, tickets to the museum itself can take up to an hour to buy when standing in line on a Saturday morning; take that into account, too. The exhibit is so popular that the museum is keeping it open past the regular closing time; it is located in a separate temporary building outside.
Also, just for guidance. The area of the city where Union Station is located is the Downtown/Loop area. MSI is in Hyde Park, near the University of Chicago (the President's old neighborhood.) You also might want to check out Millenium Park/Grant Park, which is at the Lakefront parallel to the Loop; that's where the Bean is; you should try not to miss seeing it. One Loop restaurant that is a classic that I know is open late is the Italian Village; it has a fascinating night-sky ceiling in the dining room. It's rather nice, but I still find it kid-friendly; the waiters are very kind.
If you are feeling brave about timing, there is a dedicated CTA express bus from the Loop to MSI, the #10 route. It picks up in the Loop and takes you dirrectly to the Museum. It picks up every 20 minutes and the trip to the museum takes about 30 minutes depending upon traffic. Here is the route:
http://www.transitchicago.com/riding_cta/busroute.aspx?RouteId=171 It's $2.25 per person each way if you pay cash, but I would suggest getting a CTA one-day visitor's card for each person for $5.75; you can ride any CTA bus or train all day for that price. You can order the passes online, they come in about a week.
http://www.transitchicago.com/travel_information/fares/default.aspx