I tried to do the same thing back in 2000 when I had a few days to kill in Chicago en-route to the Indy grand Prix.
The plan was to rent a 4 seater (with instructor) from a FBO at Midway, then do a couple of hours check-ride to include a landing at Meigs Field (now closed

) for a $100 cup of coffee and back to Midway. Repeat the whole thing next day with friends (not instructor) and sight see over the windy city.
Unfortunately NONE of the above was achieved. Reasons:
1) Rental from Midway was outrageously expensive (more geared to joy rides for rich tourists).
2) Public transport to Midway from the city is dire and would have taken a full day to fit in a 2 hour check.
3) Chicago turned out to have more to offer on the ground than expected, so the time flew by anyway.
In conclusion, you should have no trouble at all if you are
rich, have access to a
car and have plenty of
time. There is not much you can do about Meigs.
Hope you work something out. Maybe I should have tried harder!
TG.