Well, last time I looked cities were located in states, and no city, or municipalities can regulate by ordinance any law unless it is in harmony with state law

Therefore if the state decided you cannot detect in any park, or particular parcel of land, no city can override it
Spartacus, I too have heard this line of reasoning (and wondered if you would render it here as your answer). The rationale goes something like this:
Just as murder laws, and other such crimes, laws, codes, etc.... can not be negated on city level (eg.: a city can not "legalize murder", for instance, because it is forbidden at state and federal level). That so too do all laws subrogate down through the ranks (to county & cities).
But no, I don't think this applies to things like metal detecting. Maybe a lawyer could chime in here on this. But think of it Spartacus: There are several (lots in fact) of states of that FMDAC list of state-by-state laws, that have outright "no's". Yet as we all know, detecting goes on in those states all the time, since those laws are, AND HAVE ALWAYS, been deemed to apply to state owned parks. Not city or county or private lands and parks.
Also, think of this: park rules vary ALL THE TIME, from park to park. So just because, for example, that perhaps state parks might not allow fire-works, or off-roading with 4-wheel drives, or dogs-on-leash only, etc.... doesn't mean that other parks might not allow dogs off leash, off-road 4-wheeling, overnight camping, etc... I mean, park rules (hours of operation, and other such things) vary ALL THE TIME from park to park, at all different levels, depending on what entity runs the park. It simply doesn't follow logically that state level laws, automatically subrogate down to city and county owned parks.
Again, perhaps a lawyer can chime in about this.
And think of this: if your premise is correct, that simply because cities and counties are a sub-set of states, that state rules apply to city parks, then you have to go one step further:
The states are merely sub-sets of the federal, right? So why then, aren't we all subject to the federal ARPA then, if your premise is correct?