dmolique,
Technically to be absolutely sure, you need to check the laws for the municipalities you might travel to. As an example the City of Brooklyn has a law that forbids cell phone use while in a car.
In Ohio the State Law is defined in the Ohio Revised Code. But, the State recognizes that municipalities may have unique requirements that the State Laws don't cover. So in Ohio there is also Home Rule, which allows a municipality to create a Charter to define local laws.
Where it gets sticky is how you define whats unique to your town. Mayors and Councils tend to take a broad view of the local powers verses the state, while your local Law Director might lean towards strict Ohio Revised Code interpertation. If a town passes a law in conflict with the Ohio Revised Code the State can challenge the local law in court.
By the way, Parma does not have a Charter. There was an article in the Cleveland Plain Dealer a week or two a go regarding folks in Parma trying to get enough signatures to put a Charter referendum on the ballot. So Parma currently isn't covered by Home Rule.
FYI: I was a member of my towns 2011 Charter Commission.