Hey, just some suggestions ...
How about the city parks?
Also, how about the "curb strips"? A "curb strip" is the narrow strip of land between the city street and the sidewalk.
In many cities, the sidewalk and the "curb strip" are city property. Many homeowners don't know that, because the homeowner is always the one who gets stuck with mowing the grass in that strip. Because of that, it can feel like private property, but can be city property.
Check with your city council representative. He or she can give you the information about parks and curb strips. There could be an ordinance against "digging" or "disturbing" those areas, but maybe not.
Practice how to dig a nice, tight "plug" of turf, and how to replace it without killing the grass roots. That's a necessary technique for detecting in grassy areas. The first thing the city rep will worry about is that you're going to leave a bunch of holes in ground. When you're talking with your city person, and if the topic of "digging" comes up, it would be good to explain a bit how it's done. A day after you've left, it won't even look like you were there.
And also, mention trash. Let them know how you will always take away all the trash you find -- nails, bottle caps, pull tabs, crushed cans, foil, and other metallic junk. Plus, any other trash you see on the ground, even if it isn't metal -- for example, plastic bottles. You can't "detect" plastic, but if you see it, it goes into your trash pouch along with all the metal junk. Let them know how that stuff belongs in the city's recycling bin, not in the city's ground.
Let them know you're doing something good for the city.
Hoping it's helpful.
Cheers,
Joe