You might want to go to the Illinois forum here on TNET. There are a lot of good folks there that can help you out. I have hunted all the big parks in Chicago with good results. Just make sure you go with someone at Washington and Garfield if you venture out, those two parks can be rough at times. TMAN...
On the city and county levels, (thus, discluding state and federal from the discussion), very few city and counties across the entire USA have any such thing as "permits" for this hobby. For example, in the entire state of CA, out of 58 counties, I've heard of 2 that have such a thing. And even there, you'd be hard-pressed to find someone to card you, or a clerk who's aware of it. And of hundreds and hundreds of cities here, I've heard of 2 that have a "permit". It's 99.9% of the time, on any city or county level, simply "silent" on the issue. And sometimes you hear of a few bigger cities back east that have dreamed up such a thing, but rarely ever for smaller towns, etc... You'd be hardpressed to find any city or county that has them.
However, oddly, even though "so rare", yet the minute one DID dream up such a thing, and the minute one DOES get talked about on a forum, then presto, everyone wonders "gee, I wonder if my city has it? Maybe I should go ask at city hall" (doh )
If you're concerned that your city or county *might* have such a thing, then .... certainly .... any "permit" they issue must be listed *somewhere* for public viewing. So presumably you could look it up for yourself, at whatever the cities list of "available permits" is posted at. Ie.: their website, or down at the counter were permits are paid for, certainly they must have a "fee schedule" for the various permits offered, and so forth. If you don't see one there that says "metal detecting permit", then presto, there must not be a permit for the activity, and therefore ...... all the better