Can cities make their own laws?

Yes they can. but they cant let you do things that are already illegal at the county or state level. they can only be more strict.

The original answer above is only true because we the people, and society in general have to come to accept things as they are. We got to our current governmental system, a corporatist system, incrementally over hundreds of years. In reality in a Constitutional Republic only the Constitutional entities, the Federal government, and States governments, can make law. And only within the Congress, and legislatures can this law be made. They also cannot delegate their law making power away to other branches of government, or lower levels of government. The judicial branch cannot make law through their decisions at any level. The Executive branches, and their agencies cannot make law, which they call regulations. They cannot charge fees, aka taxes. A State legislature cannot delegate it's law making powers to Counties or Cities as well. However States can direct Counties, and local governments to enforce State laws. Municipalities in particular are in fact corporations, and their ordinances are not laws that can be applied to private citizens. They can only apply to the municipal employees themselves, and other corporations within their jurisdiction. Naturally in this day, and age you still must obey the illegal ordinances of the municipal corporation or face the wrath of the corporatist system now virtually devoid of the checks, and balances our Founding Fathers carefully put in place.