The beauty of this park is how much you can see in a half day.
From Phoenix it is about 3 hours and there is no casual camping or places to stay within the park. It is beautifully vacant. One cafe in the gift store and a few places to shop and a lot of places to learn. It is a perfect day trip from the city.
You drive up through our mountains and see the green trees and can easily find snow now and then in the winder months en route. You can grab a bite in Payson and check out the history and see how Zane Gray lived.
Then you could choose to drive up through Show Low or across a wonderful open desolate but vast Chaparral to get to Holbrook.
Most people enter up north as they see the exit and drive right on to Gallup and Santa Fe, but go to the south entrance and if you are fascinated by the actual petrified aspect, there are still legal places outside the park to pick up some rocks of your own.
Entering from the south, you are closer to the museum and really amazing logs and lots to learn. If you are NOT up for a full day, you can have a wonderful experience and still get home again before dark!
Or continue through the park drive that is well under an hour, just driving and take as long as you want at the pull outs.
You will see truly amazing stone trees (NO they are not still standing. Long ago they toppled and the minerals that replaced the wood formed horizontally, but the chunks left are phenomenal.
You might have learned all about them in the museum as you entered...) and with a very short walk, experience and ancient home of the ancestors of the cultures that still live outside the park.
A bit farther up you can view the place they call "Newspaper Rock" where those people and probably others, left their mark on brown stained rocks by chipping off the patina. Whether for self expression or communication with others or their deities it still speaks to US today.
Finally there is the last visitor center, where you can buy t-shirts, books and gas. Have an Indian Taco before you head home or off to the wonders of Indian Country.
And none of it requires anything but eyeballs and curiosity!