The FAA stilL controls the airspace. Most rules or ordinances that pertain to Drones at the local level prohibit takeoff or landing within the park.
Michigan's new law addresses these ordinances and makes them unenforceable.
tl;dr Due to recent events the current legal situation leaves a lot of leeway to state and local jurisdictions.
I'm glad to see states stepping in to do that. I would worry they might do the opposite and ban them from certain places.
Section 336 of the FAA Modernization and Reform Act of 2012 states, “Administrator of the Federal Aviation Administration may not promulgate any rule or regulation regarding a model aircraft, or an aircraft being developed as a model aircraft.” This is the act that the FAA operates under for its entire authority.
The FAA released an interpretation statement that said they had authority under different sections of the law. But a federal judge recently ruled against them. That's why you are no longer required to register hobby drones.
That said, above 400 feet agl the law clearly gives them authority to regulate airspace for safety purposes. But there is now a big grey area as to whether the authority to ban flight in certain areas rests with federal or local law, since the act specifically prohibits the FAA from regulating hobby drones.
The lawsuit was targeted specifically at the registry, but it effects other areas of the law. I don't know if the FAA has filed an appeal or not. The best way to deal with it would be to have congress remove that clause. That would make federal preemption certain, and the FAA has stated that their authority would override state and local laws. That would include takeoff/landing because their authority there for aircraft is quite clear.
Now, the FAA has no authority over photography, which is what we generally use our drones for. They could also still make laws about privacy or other uses, like stalking, etc. The FAA also cooperates with local entities for things such as noise ordinances and such. An example is wildlife refuges. FAA regs request aircraft to remain at least 200ft agl over them to avoid stressing wildlife. They will move runway thresholds to comply with noise laws. So it's unknown whether they might, at some point, make regulations to harmonize with local ordinances.