What's the cheapest transportation/stay arrangement for a guy in Northwestern Indiana (valparaiso)....?

wanting to meet his girlfriend (who's from detroit) in Chicago? Is it that she drive a rented car from detroit to NWI indiana (pick BF from there) and head to chicago together OR that she flies from detroit to chicago midway airport while he takes the train from NWI to chicago ? If not renting a car, they'd have to use cabs from/to midway airport and train station and to explore the downtown while if they rent a car, they might end up spending too much on gas (driving from detroit to chicago and then going back to detroit plus downtown chicago exploration.) I'm not sure how the cost of cabs would stack up with the cost of gas in such a scenario? What's the price range of downtown chicago hotels at the time of the year? Would you say that the whole plan would work on a budget of about $ 500 using either arrangements? It's just too many things to consider in each case !!!