Reading posts like this made me a little awkward on my first trips to the park. I felt like a criminal. WHAT LAWS WAS I BREAKING. I had read so many posts like these.
Now I just do my thing. No one cares.
I remember the first time I saw a lifeguard patrolling down the beach. My heartrate went up, I was SURE he was going to ask me what I was doing. I looked into my bag of trash for the hunk of barbed wire I had removed from the sand, ready to offer it to the Lifeguards for their blessings. I peeked under the brim of my hat as the red truck got closer, my heartrate increasing, ready for confrontation.
The truck came closer...
closer...
And drove right past without even looking at me.
Same with park maintenance, city cops, motorcycle cops, and basically everyone else. People got things to do much more important than worry about someone swinging a detector on public grounds. 99% of the time everyone is worried about their own lives, not yours.
Sure, don't break the law, do a quick search for the do's and don'ts on your city's website regarding their parks. And be about your business. Be clean and neat when detecting on public property on manicured lawns, etc etc.
I will say one thing. As a woman in the hobby, I don't feel like a creeper when detecting around playgrounds during the day. Little bit of gender bias you guys have to deal with I'm guessing

Most of the time the kids ask what I'm doing and want to know what's in the holes, and the Mom's don't make any issues.