The title pretty much says it. West side is preferred, but beggars can’t be choosers. I don’t expect to find anyone closer to Oberlin than that.
You might want to contact Grey Larsen in Bloomington, IN. Grey is a graduate of the Oberlin Conservatory, so maybe he’s maintained contacts with trad musicians in the area. Might be worth a shot.
I’m familiar with the folks at the conservatory and I’m not aware of anyone. Baroque flute - yes. Tin whistle - not so much. I’m hoping for someone whose primary interest is whistle rather than a “well, I could teach that, too.” A multi-instrumental student - the sort who was weaned on Irish music - would be a possibility. Unfortunately, the one I had went and graduated on me.
You might try some of the Irish organizations in the area. Try contacting organizations and ask for a referral if known for a whistler. There’s certainly enough Irish in Cleveland and there’s got to be at least one whistler. Try your local library and/or local schools and ask the music teacher for possible leads. Lastly, you might check in one of the Irish pubs for a whistler reference, but, you might get sidetracked in there. Cheers. 
I wasn’t thinking so much of the Conservatory itself, but the “hidden” community you might not be aware of. For example, Bloomington - where Grey is located - has the excellent IU School of Music. But Grey himself and the folk music community in Bloomington are mostly a world apart from the university. Maybe you’ve already explored the local nooks and crannies. But the worst that Grey could tell you is, “It’s been 40+ years since I lived in Oberlin, and I haven’t a clue”. In which case you’re no worse off than you already are. 
I have the name of a good teacher. I will email it to you.
Mike
Could you message that name to me as well? I am about an hour south of Cleveland, but my wife loves excuses to go to Cleveland.
Mike - can you e-mail me as well? I am looking for a low whistle teacher in the Kent OH area.
I don’t think Mike is checking the forum. I never heard back from him.