I won't comment on the reminders of home, as the link provided by Mr. Tyksins is extensive. But, as a Korean-American who has entertained several family members from the motherland, I can offer some experiences though I would not hazard to say that these are ubiquitous, as two situations were more of the whirlwind see the US in 10 days scenarios rather than an extended stay. Having said that, my experience with dining was that visiting Koreans (mine) wanted to experience things that they could not get at home - this also pertains to things to do, sights to see, etc.
So, in addition to all the Chicago specific culinary experiences, tops on the list for most of my family who came was BEEF - lots of it and in many variations. Due to the limited arable land, beef is extraordinarily expensive in Korea and not something that most Koreans eat on a regular basis or at the quality level available here. When my twenty-something cousins came to visit, we took them to Ruth's Chris, and one literally fell off his chair when the NY strips came. Then they tried to surreptitiously lift our doggie bags, claiming that they would just 'hold them for us' on our way back to their hotel. So if they are carnivorous, a trip to one our venerated steakhouses or Fogo may be an experience they would truly appreciate - or it may send their system into shock but in a good way of course.
On that same note, my experience has been that they may be less impressed with American seafood or Asian cuisines in general, as that is something that is readily accessible in Korea and generally at a higher quality level than here. Interestingly, my 10 year old cousin, whose family lived for a year in Bloomington, IL as a part of an academic exchange program, was despondent when they had to leave - not because of all the friends he would miss, but due to his cultivated addiction to Krispy Kreme.
My guess would be that if they are adventurous enough to enter a PhD program in a foreign country in a city where they don't know anyone, then you will have lots of opportunities to lead them on explorations of Chicago and beyond.