One thing that has produced well for me, which you don’t typically need permission for, is public school properties with history before the school was built. A lot of public schools were built on former farmland, and that means old houses were demolished. So check your old maps and figure out where the old houses were located on current public school grounds. With any luck you will find a nice demolished house site.
I have been detecting one of these public school house sites that I think was built 1930s (maybe earlier), and it has produced several wheat pennies (included a first year 1909) and lots of scrap brass and copper. I’m holding out for a couple silver coins. My best find so far at this site is a brass makeup compact with an 1899 Indian cent hidden inside.
So don’t think you necessarily need to get private permission to make some good finds. A lot of great sites on public property get overlooked because there is no longer a physical trace of what was there.