K.C.
(Hey, my grandma lives in Dayton lol).
The free preschool is for kids who are 4&5, who just need a little prep before Kindergarten. (hence, named pre-k). My nieces were in it and it's only 3 hours a day, 5 days a week. it's at a regular elementary school. they have afternoon classes and they have morning. they fill up quick, though, and that's why my nieces had to go out of district for it.
there is free childcare throught he government. here it is called ccms....not sure about ohio. if you want to qualify for that, then you have to be in school at least 25hours a week, or work 25 hours a week. If it drops below that, they will take your kids off the program. you can probably find out more through the health and human services in your county.