michiganer, you ask: " If it is a public place, do you automatically get permission to be there? " If you don't need "permission" to fly a frisbee, or "permission" to skip stones on the pond, then no, you don't need "permission" to metal detect at public places either.
If it's not specifically disallowed to begin with, then so be it. Read the wooden sign at the entrance to the park or school. If it doesn't say "no metal detecting", then so be it. If you're still skittish, look up the city (or county or school district, or whatever's) web site. Parks/Schools rules are usually somewhere there. Do a keyword search "metal detecting". If nothing's there, then so be it. Just stay clear of obvious historical monuments, go at low traffic/usage times, be discreet (ie.: don't be in the middle of big divots when a busy-body is watching), etc..... Be neat, leave no sign of your presence, and odds are, no one cares less (unless you're a nuisance making a mess, sticking out like a sore thumb, drawing attention, etc....)
As for private property, the best way is to catch them on their front porch (so to speak) and casually strike up conversation about the historical research you are doing. Like "I'm doing research about the country picnic site that was located back in this canyon back at the turn of the century", etc....". The reason to catch them out-&-about, is that if you have to knock on doors, that puts you at an automatic psychological disadvantage. Ie.: you're selling something, or whatever, interupting their TV show or dinner, etc.... Same with mailed letters: what do YOU do with junk mail from total strangers? Throw it away, right?