While there are good beaches on Lake Michigan, and not just Indiana Dunes, there are some decent ones in Chicago as well, you won't usually find many people on them in late September. By that point in the year, the water temperature is about 60 degree (10 degrees colder than say Virginia Beach) so even if the air temp is above average, its cooler by the lake. Fine for taking a walk along it, but not someplace you're likely going to have a relaxing beach day this time of year.