Hi, Lisa Anne,
Off the bat, I can tell you that September is a good time of year in Cleveland to plant bulbs for spring flowers and some cool weather vegetables like spinach and peas, and it's an OK time to plant perennials that are now on sale because they're leftover from the spring and summer stock at garden stores (some will get established OK and survive the winter, some might not).
Your question, though, was how to find out this kind of info for your area. The best way is probably from people who live in your area who love to garden, and Cleveland should have lots of people like this. To find them, my suggestions are:
1. Ask your question directly on the Cleveland or Ohio board of this website. If no one answers (or simultaneously) try some of the other regional boards for US Midwest, Great Lakes states.
2. Do some googling to find other gardening discussion boards with members in the Cleveland area, and ask your question there.
3. Check with your Ohio Extension Service. They probably have a website, and it may have the information you are looking for or a way to ask their staff a question. If the Ohio Extension Service website isn't' very helpful, look at the websites for surrounding states. Some Extension Service websites are very rich in information, advice and links.
4. Stop by any halfway decent gardening store or plant nursery, especially on a weekday when they won't be as busy as on the weekend, and ask the staff. I've found this to be an especially good way to learn about what will grow in my area. Maybe I've been lucky, but I've found such folks to be very eager to help and good at tailoring the information to my knowledge level, and time and financial constraints. They're also able to provide more detailed information than most books or websites about whether something will really work in the location I have in mind, because they can ask me questions and then provide a context-specific answer or set of suggestions. They can also provide time-sensitive advice, like "...but keep this inside until next week, because we're expecting frost this weekend."
4. Right now, the mega-stores like Home Depot have good sales on bulbs for spring flowers and perennials "leftover" from summer sales, and in my experience they usually have at least one staff person who knows their stuff, if you're willing to wait for them to finish with another customer or come back from a break.
5. I've also had pretty good luck simply googling questions like "What vegetables can I grow in fall?" You might try googling variations on your question, including "in Cleveland"
or "in the Midwest". The information tends to be fairly general, but it can be a good start. You also need to watch out for sites that simply steal content from other websites that might not be appropriate to your area.