Awesome!, if you don't mind me asking what national park?? I know I got lucky. I would have never found the place if my family growing up did not go camping there. We have been going for at least 3 generations.
Arkansas Post National Memorial. Its relatively small but it has excellently maintained trails and an abundance of wildlife. It's fantastic for running.
I live in the "Natural State" so there are a ton of hiking options close by.