City owned properties, public schools, and ......
QAnnesRevenge, this is amongst the places you found "no's" at, right? Then you are now the latest member of the "no one cared till you asked" club.
There probably was no actual rule that said "no metal detecting" But what do you *
think* the easy answer was going to be for a desk-bound bureaucrat? The mere fact that you felt you had to ask, simply infers that something is wrong, or damaging, or evil, that you had to ask, to begin with (lest why would you ask, if it were innocuous and harmless?). For example, would you have felt the need to ask if you can fly frisbees in the park or school yard? No. Of course not.
In the future, look up city codes, laws, rules, ordinances, for yourself. If you see no rule that says "no metal detecting", the presto, there's your answer. It's not prohibited. No need to ask "can I?" for an activity for which there is no prohibition.
The sad part is, guess what's going to happen the next time those city persons you asked see ANOTHER md'r in the park, school, etc...? They'll remember your inquiry, and think "aha! there's one of THEM", and start booting others (whom they'd probably have never even noticed or paid a second glance to).
The only thing you need to ask for is: a) if there were a rule saying "no metal detecting" (because maybe you want to find out a way-around-that), or b) private property.
Naturally ...... even if there's no prohibitions, you still use common sense. Don't go tromping around obvious historic monuments, waltzing over beach blankets at high traffic times, parading yourself in front of gardeners, etc.. Pick low traffic times, since this is admittedly an odd hobby that draws lookie-lous.