City owned? So publicly owned?
Here, if they don't want you on public land, they put up a fence and signs. If I don't see those, I assume that it's okay for me to be there. At the parks, they put up a sign saying what you can't do. If that "can't do" sign does not mention metal detecting (or there is no "can't do" sign), then it's game on as far as I'm concerned.
tl;dr version: no fences, no signs, no problems. (For land owned by local governments only. Private property, federal land, and some state land is a different story.)