Those "parkways" are great places to detect, especially if they are in an older part of town. They are even better if the city digs them up for you during construction or the addition of new sod.
I have to say, that even if the parkways are public domain, it's a good idea to get permission anyway. It is, by the way, the responsibility of the homeowner/landlord to maintain those areas, in most cases. Where I'm from, one might get shot or beat up for digging those areas without permission. Not worth the risk. Always ask.
Joe