Watch out for the state and federal parks, always best to call them to see what their rules and regulations are. I've not experienced it first hand but have heard stories of people having their metal detectors confiscated for getting caught detecting in a federal park. Some state parks have detecting permits you can get, others are off limits.
If you're into older coins you may want to head to the library and check out the local history section to see if there are any locations where there may have been an amusement park, carnival, fairs, old swimming holes, train stations, church orchards, sled riding hill... Any place you can think of where there was activity long ago that may have involved money changing hands.
Dudes