The places to look in the woods (or ANY type terrain, for that matter) is: wherever people gathered, played, ate, slept, recreated, etc... in the past.
You don't just go out into "random woods" or "random desert" etc.... to hunt. There has to have been some reason for hunting there. Eg.: a stage stop, or a camping grounds, or a foundation evidencing a pioneer habitation, or a defunct park, etc...
Perhaps in Europe they can just go to any random furroughed field or forest and eventually "find things". But that's because they've had thousands of years of history there. So just random furroughed field losses of coins can occur. But here in the USA our history is much to short. So you've got to research to know where stuff went on in yesteryear. Also has to be post-european contact, of course, since the indians here had no refined metals.