....Everything really....
Tenn, that's much too broad of a question, to say "everything". Because there are multiple levels of govt. land. And even WITHIN each entity (state, or fed, or county, or city), there are even THERE going to be various types within each category. For example: city parks may not allow dogs, yet city sidewalks may allow you to walk your dog down the street. Or county parks may "close at sunset", yet on a county road, you may be able to waltz down the sidewalk along that county road after sunset, without being "afoul" of this "closed at sunset" clause (because one rule dealt with parks, while the other was just road-right-of-way).
So for someone to simply say "all federal land is off-limits", or "all state land is off-limits" or "all city or county land ...", well, you get the picture; it's not true.
And once you get down to county and city level "rules", well go figure, the state of TN has oodles of various counties, and hundreds upon hundreds of cities, I suppose. So to answer "everything", is much to broad of a question. You'd have to say specifically which city or county, and even then-so, which type land within that organization. Ie.: a school? a beach? a park? a road right-of-way? an emminent domain vacant lot repossesed by the county for lack of tax-payment? etc.. etc... etc....
That's why I asked, in my original answer, where/what you meant.
Forgetting for the moment fed and state, and focussing just, instead, on city and county level parks (or whatever types land they manage within their jurisdiction): There is RARELY ever anything specific saying "no metal detectors", at any city or county level anywhere. Once in a
great while, you'll read of some city or county having some sort of a rule, or some sort of a permit. But those are the exceptions. Perhaps a bigger metropolis, or some sort of county with oodles of sensitive historic monuments. But 99% of the time, local codes, laws, & rules are simply silent on the issue (dont' say anything, either way). Thus as long as you're not being a nuisance, sticking out, begging for attention, leaving holes (or lacking the discretion to go at low traffic times to avoid such lookie-lous), then usually you won't have any problems.
To know whether your county or city has any such specific rules, saying "no metal detecting", it's a simple matter of looking it up! (not asking someone "can I?"). The city or county codes are available for public viewing somewhere. Like down at city or county hall on the front counter for public to view. Or if they have a web-site, the park dept's rules will usually have a sub-section detailing the codes, laws, etc... Eg.: no camping, fires in pits only, no off-roading, closes at sunset, etc.... If you see nothing saying "no metal detectors", then presto, it must not be prohibited

The worst that can happen then, is if someone "has an issue", they're welcome to tell you. Then give lip service and move on. You can tell them you looked it up, and saw no prohibitions. And no, I do not consider verbage about "defacement" "alterations" and so forth to apply to us/me. Because all such wording inherently applies to the
ENDresult, right? Ie.: if you leave the area exactly as you found it, with no trace of your retrieving, then presto, you have not "defac
ed", or "alter
ed" anything, now have you? Sure someone can argue semantics about the temporary evil process of extraction if they want. That's why I say to pick low traffic times, and not be waltzing over beach blankets at an archie convention. I've even gotten to where I hunt parks, schools, etc.... at odd/off hours: early AM's before 8am, after dark, on holidays before noon when everyone's still sleeping in, and no park or city staff is working d/t skeleton crews on holidays, etc..... So peaceful, so serene
I have things to say about the fed, and state level too, as it pertains to your question. But for now, start with this, and let us know if you have any more questions.