Methodist on Euclid has a wonderful 4-day program for kids who miss the cut-off. My two both went there for three years each. Only local preschool that is NAEYC certified. It pulls from a bunch of different neighborhoods, so the kids wind up having friends at their grade school and others the following years. This has been a huge plus for us, as our girls have become more involved with park distict and dance programs - they always know someone in the class (usually from proeschool). Methodist also has a full playground for "outside time" on warm days which is not the case for some other local programs. Kids can also stay for lunch, Spanish, Kindermusic, or additional play time. ###-###-####.
good luck and welcome!