Technically, the NP are not no fly zones - they can prohibit the launching and landing of drones within the park, but can't control the airspace over it. Only the FAA controls airspace, so if you can take off and land in, say a public right of way along the park entrance (outside the park) you can fly - legally - all you want. Be aware of laws about harassing wildlife, disturbing nesting raptors, etc. though. Those restrictions can also bite you.
In my state you CAN fly in state parks, but you have to jump through hoops to do so. I just wanted to fly my new Mavic around a park last spring. Following the law, I contacted the park manager, filled out the forms, and was prepared to send them in with $25 (to fly for about an hour!), when I was told I'd need a $1 million insurance policy! WTF?? This was also before you could get insurance online in advance with the Verifly app. You had to show proof of insurance before they'd approve the flight. "Crap," I said.
When our friends and us arrived, there were two other campers in the entire park, and they were out fishing. The two young rangers at the park were picking up garbage and watching TV at the entry station. Not another soul in site. Hmmmmmm.