There is also a preschool in Wash U medical school area, near botanical garden, I know a lot of chinese who work in Medical school send their kids there, which is a lot cheaper -- 365/mo from 7am-6pm-- 4 yr ago price.
If you move from University city to the Clayton -- the school district is much better.
You can put your kid in preschool, then enroll him or her to public school next Sept.
是不是上私利就可以上kindergarten --- you can check with the school you interested, but I don't they have different bar.
Good luck.