Steve, I will chime in to your question, by commenting on treasure-hunter's reply:
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Oh boy here we go again....LOL." Yes: you will get answers and opinions that start from: "get signed written permission from the mayor to detect even a park sandbox ..." and to the other end "nah, if it's public, and not posted, go for it".
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I recommend you go to the thread for your state ..... " Yes perhaps. But those forum subsections get very little traffic. And since the question really, is not limited to just
state-owned property, and in effect reaches down to
city level schools and parks, then the national forum (ie.: cities
in general) then the main page would get relevent opinions from others.
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Some local schools allow it and in other states they don't, you have to check you local area" The only thing I would add, with "
checking" at local city park and school levels (if you are skittish) is to look it up for yourself. Ie.: don't approach it from the "can I metal detect?" perspective (as if you were asking permission), because you might/can merely get a "no" from a desk-bound clerk whose image is geeks with shovels (when no actual rule exists, nor would she/he have probably ever noticed or cared ..... till you asked). Rules are usually written on the sign at the entrance to parks and schools. Or do a key-word search under "metal detecting" at the city website, etc... If it is silent on the issue, then I would consider myself no different than a kite-flyer, frisbee thrower, etc... They need not "ask", nor will I. This is assuming of course you intend to do no harm, leave no marks, etc....
Personally, I hunt parks and schools anywhere and any state I go to, unless it is specifically posted, or an obvious historical monument, etc.. But the psychology applies: whenever you swing that "wand" thing, curious lookie-lous will be attracted, and you might get a busy-body nosing in
So don't go during crowds, go at off-hours, etc....
Oregon (as with all states) might have things on "cultural heritage/historical artifact" type verbage. Ie.: coins or items over 50 yrs. old, etc... At that point, it's up to your math skills 
Or as per jewelry, there is probably in every state: lost & found laws (items over $XX value have to be turned in to the police dept, etc...) That's a whole other thread though! 
