to South Haven
along the lake front, the total driving distance is 126 miles - a driving time of 2 hours and 40 minutes. I have not done this drive. My suggestions are from Google Maps. Leave Chicago and drive down to East Chicago on US 41 and US 20. Then there is a short section of I-90 and then US 12 and finish up with I-94. You could take US 12 farther, but it goes through the Indiana Dunes National Park and there appears to be an entry fee. Otherwise you can take US 12 most of the way.
South Haven is 1 hour ahead of Chicago. I don't know what you mean by cheap. The amount of expense will be how much gas your car uses and whether you stop and spend money anyplace.