Yes - Depending on the city, most Parking Strips or Easements are Public Property, as is the curb and gutter and the sidewalk itself. Some cities even own 12-18" on the private property side of the sidewalk to allow room for sidewalk work if ever needed.
HOWEVER - and this is a big HOWEVER, all the cities that I know of require the adjacent landowner to care for the parking strip, keep it cared for and not place anything in it that would impede access by a utility company (usually the water company) if needed. I will retell a bad and somewhat embarrassing experience a very long time ago so that none of you have to repeat it.
A little over 20 years ago, a friend and I had selected an old area of Salt Lake to hunt some private residences. The area dated back to the mid-1800's and had produced really well in the past. A couple owners weren't home and the others fell through so we were now going by the seat of our pants to find a place to hunt. An old home caught my eye and I opened the gate and walked up to the front door and knocked. Nobody answered the door though I could hear activity inside. I rang the doorbell and nothing. I waiting a polite amount of time then left the front door and yard and closed the gate behind me. In front of me was the sorriest excuse of a parking strip you could imagine. It was all weeds mixed in with a little grass for background. It didn't look like it had seen any care at all for a very long time. In contrast, the yard behind the gate was well cared for. Obviously, I ASSUMED, the parking strip area was abandoned by the owner.
So, being the bright individual I was at the time, I turned on my detector and started hunting. Some old coins and a nice trade token surfaced in the first ten or fifteen minutes. My enthusiasm rose, it was going to be a good day. It wasn't long until I heard the front door open and a very angry man marching at me with a mouthful of expletives that would embarrass most individuals. He got right up in my face and called me every name in the book and told me to get the !@$#$%&^$$ off his property.
A number of responses went through my mind. I started with, "I am sorry", "I knocked on your door to ask if you would mind", and so on. He wanted nothing of it. He kicked in with the language full tilt, and I finally lost my cool and told him, "You know what, this isn't your property, it is public property and since it appeared that nobody was caring for it, I didn't think anybody would mind". That only angered him further and he called me more names and told me if I didn't leave now he would call the police and have me arrested. I was pretty ticked off at the guy by this time and wanted to make a point, so I told him that if he wanted to call the police, by all means call the police. I will be happy to wait until they show up. He called me more names, turned and went in the house. My friend came down the street from where he was hunting to see what was going on. He gave me that look and turned around and went back up the street.
Well, I continued hunting the parking strip, making sure there was no sign of having damaged a single blade of weed or grass and I waited and waited. Finally, after what seemed a good hour, a police car drove up the street and stopped in front of the house. The owner came marching out of his house madder than all get out. I waited patiently across the street listening to him rant. He walked with the officer over the entirety of the strip looking for some place where I had damaged his 'grass'. They couldn't find any sign that I had been there. Inside I was pretty pleased with myself. The officer talked in quieter tones to him for another five minutes or so and the guy obviously wasn't happy. He then stopped and came over to talk to me.
I introduced myself, offered some identification and an apology over the situation. The officer agreed that I was in the right and that there was no sign of any damage to the parking strip, but he continued, this could have really got out of hand. Under the circumstances, he thought it would have been best to avoid the confrontation, rather than escalate it. He said the homeowner was angry enough he may have done something really stupid. I didn't think about that. I was caught up in my pride of being right. Too, I didn't think about the repercussions of the situation. What if this guy knows somebody in the city and was able to get metal detecting banned on all parking strips or on all public property for that matter. And I didn't think that maybe I put the homeowner in a very awkward situation. Most don't know that the Parking strip isn't theirs. As far as he knew, I was on his property. I was really way out of line. I didn't think very far ahead and I certainly didn't do what was right.
Now, I take the time to ask and gain permission to hunt the easements. In fact, I will usually ask to hunt the yard of the home itself and if that doesn't work out, I ask if it would be ok to hunt the easement out past their property. Usually if I can't get permission for the yard, the will grant permission for the easement.
Just a thought as you go out there. Be courteous ... good luck.
