I wouldn't swim near the lighthouse. It's pretty rough. But, in general, lake Erie is ok for swimming, just don't get in your mouth or swallow.
No,it's way too rocky. You can go to the east side of Catawba Island to the state park and swim, or to Crane Creek which is west towards Toledo by Maggie Marsh, Port Clinton has a small beach, and there is Maumee Bay State park.
He is correct water is rough and rocky not much of a beach there
I'd suggest a water test for your peace of mind.
I wouldn't recommend swimming in it. Just my opinion.
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