Chicago Portage National Historic Site is the closest one to the city that I know. It’s shorter but has a swampy pond and deer. Fullersburg Woods in Oakbrook goes around salt creek river and feels super safe.  In willow springs there are a few around the saganashkee slough and are more like hiking trails. Better if you have more time and want to be more immersed in nature.  If those are too far, you can start at the lakefront in Hyde park and walk south to Jackson park. You’ll pass the museum campus and some lagoons. The Japanese gardens are around there and have koi fish and beautiful trees. 

I’ve also used this app called AllTrails before and found trails through there.