desert vet, penny farmer and Rginn give good answers so far. There are very very few cities across the United States, that have any prohibitions on metal detecting. It is simply an un-addressed issue at most all city-levels, since it's such a niche hobby/rarity, and for the most part, considered innoccuous (unless you're being some sort of nuisance, leaving a mess, raiding obvious historic landmarks, etc....).
The reason penny-farmer says not to go asking, is because sometimes you can get a "no", where no real prohibition exists. Ie.: some deskbound clerk whose image is geeks with shovels, will simply spin their own opinion, saying "no" because you might bother the earthworms or something (mind you, all the while, where no one might actually care less, or ever have noticed you). So the better way, if you are skittish, is just to look at the city websites list of park rules (city ordinances, etc..). Do a key word search under "metal detectors/ing", for instance. If it is silent on the issue, THEN SO BE IT. You wouldn't ask permission to fly a frisbee would you?
Now this is not to say that you will never get a busy-body nosing in, in the field. Because let's face it: you're in an odd hobby that draws the stares of the curious, right? And there's always the connotation that you will leave holes, marks, or whatever, right? (which of course, you won't leave any trace of your presence). So a little discretion is in order here: Even though there may be no prohibitions (so long as you're being neat and clean), yet you still want to pick off-times, low traffic, etc.. So for example, if you arrive and see an entire maintenance crew working on that park, on that day, well ..... pick another park for the time-being, etc.....
