uh, curious first: When you say you "have permission for your city parks", then.... if you felt it was necessary to have permission for them, then why wouldn't the same logic apply to other forms of city land you list ? Eg.: town commons , city-green belts, curb-strips, etc..... ?
In my opinion, you need(ed) permission for none of them. No-more-so than you'd need permission to fly a frisbee. All you need to do is look up for youself if there's some sort of municipal code that said "no metal detecting" . If not, then there's your "permission".
Naturally, since md'ing has connotations (someone might think you're about to leave a mess), you need to avoid being a sore-thumb. Ie.: pick lower traffic times, avoid lookie-lous, etc... And of course, if any of the places you had in mind are obvious historic sensitive monuments, then that would be a different issue. But for run-of-mill green belts and town commons, parks, etc... I never ask. Lest you risk running afoul of "no one cared ... UNTIL you asked" phenomenon.