In NY state, you gotta get a permit to hunt NY state parks. I learned this by getting kicked out of one long ago. So, I buy a state metal detecting permit if I want to hit the NY state park water or beach. I think it's about $20 per year. Yes, the usual rules about finds, "if they are worth more than xx dollars must turn in to the park police" on and on...
In NY state parks, you can't dig turf, only sand or in the water. Period. What this law is saying is that people don't like to see signs of metal detecting, like big holes and ruined landscaping and leaving big hunks of metal on the site.
I have never had a problem hunting my local city parks or public gathering places (sports fields, playgrounds, fire halls).
I did get kicked out of a city school field once, but have hunted them many many times before and many times since. I just don't argue and I leave and be as polite as totally possible. The guy was just a minor employee on a power trip.
I always keep a low profile when hunting non-restricted places. Nowadays, I have better luck in the woods, just off the beaten path. Usually, nobody even knows I'm there. If I'm gonna do the turf in parks, I just go when nobody is around and when its wet to minimize sod damage. Try to keep a goodly amount of trash metal in your pouch just in case. I always-always-always fill in my holes with care. But remember, just because the site is not posted, doesn't mean you wont pi&& off someone that wants you gone (for whatever reason). If this happens, just show him a pile of crappy metal in your pouch and be polite and apologize and just leave. DO NOT ARGUE WITH ANYONE. They don't want to hear it, they just want you gone. If you are nice about it, the only thing he will remember is all the trash you took out and he's gonna think metal detectorists really are not bad people, they are just like everyone else. Anything that we can do to stop anti-detecting should be on all our minds. Learn the rules and the positive aspects of detecting, pass it on, and try fighting the lawmakers the easy way.