Hi C.,
I'm not sure if you're familiar with the book called Polar Express. Well.... this story would tie in nicely with a train ride. Especially one that has Santa aboard! Check out this website for more info. They do this in many states now.
http://www.traintraveling.com/events/polar-express-trains...
My friend took her son when he was 4 yrs. old and he loved the ride with Santa. Okay... but you're asking for things to do once you get to Chicago.... Okay.... I would suggest taking him to Rainforest Cafe for lunch or dinner. They have volcano cakes that you can get and the waiters will come to the table with it and sing happy birthday. The decorations in the restaurant are totally geared for kids with animals chirping, sqwauking, singing, etc... and many large fish tanks. It's on Clark Street. Here's reviews on this website:
http://www.kidwinks.com/KidsRestaurants/3/RainforestCafe/...
And on this website, you'll find more ideas! I love kidwinks.com for finding places/ideas for kids.
Navy Pier is good, too. (especially in the warmer weather because you could go outside and ride a boat, ferris wheel, etc... but okay it's Fall now!) They have a fun maze and a really good hands on musuem for kids there. Do an online search for coupons for the fun maze. It's around $10 each but there are buy one - get one coupons out there on line sometimes. (But I think your son would be free because of his age. Yay!) http://www.navypier.com/things2do/rides_attract/amaze_chi...
The Shedd Aquarium is nice too for 3 yr olds. Bring your stroller though because he may get tired since it's pretty big. There's a really cool toy store on one of the busy streets... that would be cool for him to pick out his birthday present in there. http://www.sheddaquarium.org/
Enjoy your day in Chicago! I'm sure your son will have a fun time! I think one or two other places besides the train ride is plenty for you son for the day.
J.