You can get into ballet at most chicago park district locations at 3 but soccer is usually 4 and up. Ballet at Peterson Park Gymnastics Center is $40 for March 31- June 7 and is low key but on a wood floor with barre and mirrors. Online registration already began on Monday, so if those times are full, in person sign up begins tomorrow from 2pm-4pm and weekedays after that. Go to Chicagoparkdistrict.com.
Another idea is on Devon, in Edgebrook. It is called the Dance and Music Academy. it is more expensive ($90) but the summer session is cute for 3 and 4 year olds with a Cinderella or Sleeping Beauty theme. You can watch via closed circuit TV in their waiting room at that place.