Chicago is the best family vacation spot! You don't need a car, there are tons of free activities: Lincoln Park Zoo, beaches, festivals (ethnic, neighborhood, music, etc.). Great museums (with lots of free days)
what is not too much money? how old are your kids? What do you like to do?? I live and travel the Midwest. My kids are teens now. we like to tent camp on lake Michigan. go to Cedar point. Put-In-Bay is cool, but not on a weekend for kids.
Chicago was great, Wisconsin Dells was really cool. I could go on and on but not sure what you have in mind?