Does the code for your town say no metal detectors are allowed in the park? Or does it say no *digging*? Or no *disturbing* the soil? No *removing* the soil? If metal detectors are not mentioned specifically, it could just be the ancient law against property damage that has always applied everywhere.
Just note the exact wording for each town under park & rec rules & check the city codes online. Best not to call the desk bound bureaucrats that will just give you a no based on the ancient property damage laws. Besides city parks, there are county parks & state parks, but city parks are least likely to truly prohibit detecting.
In some cities with more than 1 park, 1 could be off limits as a historical or archaeological site. Also, a few large cities could have a privately owned park, like Tower Grove Park in St. Louis. Then there are places listed on the National Register of Historic Places, which tends to emphasize buildings. But sometimes entire neighborhoods are off limits (rare). National Parks all off limits & National Forests are risky, too.
Public schoolyards are generally open to non-damaging detecting. Religious & other private schools are places they can prohibit even neat detecting if you don't have permission. It's hard to get permission to detect private or state universities. State fairgrounds are generally off limits, too.
Missouri had about 3,400 populated places in 1890. Some of these are now ghost towns (permission needed), some are still tiny. Some had steady growth & some are mostly new, like many suburbs. County fairgrounds if not posted are probably detectable & size can be anything from under 15 acres to over 300 acres.
Wikipedia has histories of nearly all towns population 10 & up, plus true ghosts. hometownlocator.com is a good site to tell if a site is totally abandoned and if anything still shows. It lists things like schools, churches & post offices that are no longer there, & cemeteries that may have been part of a town no longer there. Their town populations are all for the last July 1st.
County websites will often have park/school/history info for each town, & have tax assessors info including acreage & year each house was built. historicmapworks.com & other info on maphistory.info can be very helpful. Best wishes, all!