Yes, as Larry says, there is an alphabetic list on the FMDAC site. I don't have the link, but you can find it by clicking around on their site.
Keep in mind:
1) This would only be for state level land, and have no bearing on city, county, federal, private, etc... land.
2) The way the list like that was developed, years ago when someone put it together, was innocent enough: They asked! Ie.: send a form letter out to all 50 states park's dept. headquarters asking something like "what, if any, rules are there regarding metal detectors on state land in your state?".
Sounds reasonable enough, but this is where it gets funky: Some of the states who may have responded with "no" or dire sounding restrictions, were places where ...... prior to this ....... people detected state parks all the time, with no problem. Ie.: it never even occured to people you needed to ask, or that anything was wrong, to begin with! So I guess when you ask a bureaucrat, in a stuffy office somewhere, you can get a "no", simply because they morph something else (cultural heritage stuff, don't disturb the vegetation, etc...) and simply give the easy answer? (when in fact, no one really cared or gave it thought before).
I know this is true for CA state parks, for example. There are some you can detect openly, (yes, even right in front of rangers) and no one cares. Yet if you read that FMDAC link on CA, you might think you were severely restricted or whatever. State beaches for example, are routinely detected here (FMDAC link not withstanding), and no one's ever cared. Yet I have no doubt that if you asked enough questions, high enough up the chain of command, you'd probably find someone to tell you/me "no".
For this reason, I take that FMDAC link with a grain of salt.