We love visiting aquariums – and there are a few good options within driving distance of Madison, WI. Milwaukee and Dubuque are each about 60-90 minutes (depending on what part of Madison you are starting in) and Chicago is a little over 2 hours. All doable for a day trip (or a quick overnight!).
My family became members at Discovery World several years ago and we love that it also includes an amazing aquarium!
Reiman Aquarium at Discovery World 500 N Harbor Dr, Milwaukee, WI
Shedd Aquarium 1200 S Lake Shore Dr, Chicago, IL
National Mississippi River Museum & Aquarium 350 E. 3rd St, Dubuque, IA
Milwaukee County Zoo Aquatic & Reptile Center 10001 W Bluemound Rd, Milwaukee, WI
Racine Zoo Discovery Center 2131 N Main St, Racine, WI
Henry Vilas Zoo 702 S Randall Ave, Madison, WI