Let's get something straight. The 2nd amendment is very specific where it prevents the Federals from passing such laws. The Rtwinggunnutters go off so much that that's over looked. It's the States responsibility. As District Court Judge Young said, "If you don't like the way your state's laws are, move".
The Tenth Amendment speaks of powers (rights) that belong to the federal government, that belong to the states, and that belong to the people.
To whom does the right to keep and bear arms belong? Does the Second Amendment speak of a right of the states, and forbid that right from being infringed?
One must look at the original intent. Only then does the wording of the 2nd amendment make full sense. It was written to prevent the Federal Government from disarming the States and the Citizens. The biggest failure of the Articles of the Confederation was that it did that too well and left the Federal Government completely at the whim of the state. That was pretty well corrected in the United Stated Constitution. Or as near as humanly possible. From 1791 to about 1916, the Federal Government couldn't even legally put up an army with enough force to defend the nation without the states providing the troops. Yes, Dorathy, most of the Union Troops were sent by the States for the Civil War.
The State has to decide what is in it's best security interests. The Federal Government is barred from doing that. We just went through a period where the Federal Government sent in it's own "Troops" into the Cities without the States permission. Luckily, the States stood up and said, "Enough". It proves that our Federal Republic works.
Now, to answer your question. If a State makes gun laws, no city, perish, town or county can override those laws. Some have tried and received rebuke in the Court Systems. They can add to but never attempt at reversing the States laws. Only through a state wide vote can that happen or in a State Legislative/Governor venue. The days of the helter skelter gunlaws ended when Heller was handed down.
Heller ruled that inside your own home, you had the right to have a "Normal" weapon (meaning a conventional defense weapon) to defend your home against intruders. It also ruled that the "State" can require you to have special licensing and storage if it's deemed necessary but those licensing and storage cannot exceed a citizens means to obtain them. To be specific, it ruled that a normal Handgun is applicable. Now, the States can expand that to include almost any other weapon. But the word "Normal" comes into play. And the Courts have ruled what is Normal using the "Heller Law". Many states do not require you to have any special licensing to have a gun in your home. Heller merely ruled that the Stated "MAY" require it. Just like many states have limited the number of rounds any weapon may have in it's cylinder, tube or magazine. The 22 cal tube fed rifles being the exception.
You have the right to protect your home and family against intruders. That is the only real right you have. You have the right to have any "Normal" weapon to do this job with. Sorry, the the AR has been excepted from the "Norm" on this one. But it's the State that deems what is "Normal", not the Federal Government whom the State must guard against the Federal Government form becoming so powerful that it can military overthrown any given state. We have just came back to the 2nd Amendment and it's original intent.