It should be fairly easy to fly into O'Hare or Middway on Friday Morning or early afternoon, then take the "L" to Union Station. It's been probably 10 years since I've lived in Chicago, so I'll let someone else share the details on the ins and outs of taking the "L" from the airports to the train station. It's not very difficult to do. The train out on Sunday Morning leaves at 7:32AM, early, but it should give you some time to enjoy lunch in Chicago!
As for Amtrak, the Hoosier State departs from Chicago at 5:45 and arrives in Lafayette at 9:58PM. There's two cab companies. City cab 765-477-1234 or 4 Star Taxi 765-742-8400. Purdue unfortunately isn't all that close to the train station so I would suggest to take a cab. As for saving money, as far as Amtrak is concerned, book your travel early to get the low bucket fares. Lafayette isn't a very expensive town, and if you're staying courtesy of Purdue, that should save you some money. It's been a long time since I was in college, but Purdue and the towns are impressive. My wife and I have enjoyed the town and the people here.
This next paragraph talks more about Lafayette/West Lafayette in general...it's not specific to the poster, but more of a lay of the land around Lafayette's train station. It's good information for anyone interested in taking a train ride to Lafayette...
Downtown Lafayette is right on the East side of the Wabash River, and the train tracks and station is right on the river. There's actually a very nice river walk across the Wabash linking Lafayette and a shopping complex called Wabash Landing right at the station which gives access to West Lafayette. At Wabash Landing there's a Hilton Garden Inn, a movie theater, a couple of restaurants and some stores and that's not a bad walk from the station at all. Downtown Lafayette is also a nice area with a variety of bars and restaurants and shops and stores. There's lots of live music and not being too close to campus, I wouldn't call most of the bars on the Lafayette side campus bars. I mention this more to give a feel for the town, and for anyone who might be inclined to take the Hoosier State in for a train ride and a nice visit. There's also the Holiday Inn City Center a 3 block walk from the train station on the Lafayette side. Both the Hilton Garden Inn and the Holiday Inn City Center are going to be the more expensive hotels in the area, with more budget conscious choices out by Interstate 65 on State Road 26.
Good luck, I hope your stepdaughter likes the town.
My stepdaughter is looking at taking a trip to check out Purdue University. We have been checking different transportation options and are thinking of flying SWA from OMA (Nebraska) to CHI and then taking the Hoosier State to West Lafayette. Our return would strictly be all by rail with the Hoosier State and CZ back to where we live in LNK. We would need to find someone to drop us off in OMA (50 miles) so this would work. How far is the Amtrak station from the campus? Is there taxi's? Any other ideas to make this work as much as possible for a low amount of money. I think the school said they have housing/hotel for us to be put up in on Friday/Saturday. We are thinking of leaving on a Friday out of NEB and returning on Sunday back to LNK. Thanks everyone!