In most states these are city property, not private, and most do not ask permission nor need to but try to explain that to a few homeowners that cut the grass on them and assume they own them and you might be in for a fight or a conversation with a policeman.
Some do ask permission and might get a lot of nos but that can also lead to permission to hunt the rest of the lawn so different opinions about that permission stuff.
Many never ask and never had an issue or if they ever did get hassled they just move on...there are more out there than we could possibly hunt in our lifetimes so the numbers are in our favor for those that have the courage to do it.
Many hit these things exclusively, we call them curb strip hunters, and have done very well especially in older neighborhoods.
I hunt them in my neighborhood from time to time.
I have found old tokens, some jewelry, casino coins, regular modern coins and older coins including silver.
I even found a civil war three ringer bullet in one once.
Areas near where people walk on sidewalks can be great, where people pull out their keys from pockets walking to their cars other things can come out of those pockets along with those keys and jewelry can fall off so these can hold plenty.
Here is a great thread about hunting these things.
http://metaldetectingforum.com/showthread.php?t=202666