If a lot is unfenced where an old house has been demolished, and I see no signs or fences, I certainly wouldn't hesitate to hunt it. If it had those old wooden veranda style porches, check underneath where those used to be.
As far as public locations (you asked about "permits"): If you are skittish about public parks, school yards, etc.... Go to the city (or county or whatever the case may be) website, and usually the laws, codes, regulations, etc.... of the city and/or park's dept's are posted there. If you see no mention of "metal detecting", then presto, I guess it's silent on the issue. And if there are no prohibitions, then no need to ask further, IMO. In the same way that you would assume you can fly frisbees in a park or school yard, if you saw no rules prohibiting it, for instance.
