According to the Burpee site, it can take 80 - 120 days for a sunflower to flower. The first frost date for Ohio is in late October which means it is probably too late. Next year, you should plant every couple of weeks until the end of June.

You might get away with a few of the dwarf varieties in a southern exposure, if you just want the flowers--the seeds on those are strictly for the birds! :)