Aside from the state and federal level parks/property, for the moment, ... when it comes to city and county parks/land/property, just do this: Most cities and counties nowadays have websites, right? Just go to it, and there's always their codes, rules, laws, etc... for their geographic locales. Just do a key word search under variations of "metal detectors(s) ", etc... If it is silent on the subject, then so be it. Then there must not be any prohbitions

And if there is no website with their local parks and city rules, then the information must be on the desk at city or county hall, since it's public domain info. It's usually set out on the front desk, for instance, for public viewing. Scan through it, and if you see nothing that addresses detecting, then presto, it must not be prohibited.
Of course use obvious due discretion. Don't be a "sore thumb" at high traffic hours, etc... We're in an odd hobby that draws curious lookie-lou busy-bodies, who might make assumptions or conjectures (ie.: you might harm earthworms, you might make a mess, blah blah). So go at off times, don't go when during an archie convention waltzing over people's beach blankets, etc....