According to Google Maps, the driving time between Midway Airport and Waukegan is around an hour and 15 minutes, and approximately 45 miles, or more depending on your route.
About 100 miles.
If you're looking for a route, I would suggest taking Cicero Ave. North to I-55 South to I-294 North to Grand Ave. exit eastbound.
Midway Airport
Both airports have excellent public transportation to downtown Chicago. Either one really. O'Hare has more flights, but Midway typically has lesser expensive flights. I live in the far North suburbs, so Midway is farther from me, but I will often use Midway because of lower fares. I also find that Midway is a bit cleaner and more organized than O'Hare. This is likely because of it's smaller size.
Chicago Midway: IATA: MDW ICAO: KMDW
There are two airports located within the City of Chicago: O'Hare (ORD) and Midway (MDW). Gary/Chicago International Airport (GYY) is located in Gary, Indiana but is run by the Gary/Chicago Airport Authority. There are also other, smaller airports near Chicago, such as the Chicago Executive Airport (CXE) (formerly Palwaukee PWK), Waukegan Regional Airport (UGN), and DuPage Airport (DPA).
Midway Airport is approximately 10 miles from downtown Chicago.
It is 356 miles according to Google Maps.
Midway Airport is in Chicago; it's about 11 miles from the heart of downtown.
It is Queen Beatrix International airport.
Midway International Airport is located in Chicago, Illinois. It is the second largest airport in the entire state of Illinois, after Chicago O'Hare International Airport, and is the largest airport in metropolitan Chicago.
It is 41.4 miles according to Google Maps.