not only are the strips between the sidewalk and road public, but in mass. at least, the law states that ten feet from the road is public. No one can tell you to get away from the grassy strips. just be prepared for a few annoying people to either complain or call the cops. My advise is for you to stop in at the police station in the town that you want to detect, that way they know who it is in case someone complains. if you know the cops before you start, it wont be so shocking or as much of a hassle if a cop car pulls up along side while your in the middle of lifting a plug and preparing to dig on the side of the road.
Although it belongs to the property owner, the city has a right- of- way easement mainly for utilities. Consequently you are not allowed to build on the parking or obtruct it in any way. The public has access to the parking but only as a thoroughfare and in my jurisdiction would have to have the property owner's permission to detect on it. Here an easement is generally 12 feet from the curb line, but streets with no curbs, the easement is measured from the center of the street depending on the width of the street. The width of the easement can vary and it depends on how the street and property was platted back whenever. It can get pretty confusing but can be figured out by looking at the plat maps of which every city, county, or parish should have a set. I would imagine the rules governing that area will vary from state to state, city to city, etc, but would be similar. 
