I'm not sure where in Kenosha you are playing baseball. The City of Kenosha is located in Kenosha County. I live 9 miles south of the Kenosha County line so I know the area.
Here are some options:
Happy Acres Kampground is in northwestern Kenosha County.
Richard Bong State Recreation Area is in northwestern Kenosha County.
Illinois Beach State Park is in northeastern Lake County, Illinois, just south of Kenosha.
Chain o' Lakes State Park is in northwestern Lake County, Illinois, just southwest of Kenosha.
Sanders Park Campground is in southeastern Racine County, just north of Kenosha.
Cliffside Park Campground is in northeastern Racine County, just north of Kenosha.
I have personally camped at Illinois Beach, Chain o' Lakes, and Cliffside within the last 5 years. I hope this helps.
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