On a budget, weigh it — Indiana Dunes (day-trip) isn't cheap for what it is.
~$25/vehicle or train fare
A genuine national park with towering sand dunes, swimmable beaches, and skyline views back across the lake — and you can reach it by the South Shore train without a car. The honest catch is that it's flanked by steel mills, so the setting is mixed, and like all of the lakeshore it's a warm-season pleasure.