I visited the Park 'proper'. I don't remember birds but I remember a whole lotta nature. I rode my motorcycle through there thirty years ago. It was lovely. The rangers promised to watch my bike and I signed out for hiking into the region for a night. I only had a flexible Vietnam style 'bag' canteen which could carry a liter no more, so I made myself down a liter of water beyond my thirst being quenched. Hiked in in the afternoon, enjoyed the petrified bits of wood which I left alone, and the myriads of small cacti and succulents which struggled and throve. There was some clambering, and mostly hiking into a flat-formed valley with some dry washes, which term also applies to the subtle yet quietly dramatic coloration of the hills. I climbed a hill and watched the sun go down. I thought I was alone and the experience was deeply spiritual and personal. In fact, I was to meet up with a couple who were camping in the valley not far from me. They told me they had got a photo of me silhouetted against the setting sun with my arms outstretched. Sounded too good to be true, and though we traded addresses I was never to see it.
That part of the country is incredibly beautiful and not overcrowded. Research the routes a bit, but don't overplan your trip. Just go, spend time there, and may you have good weather. If you're up to some hiking that will magnify the experience manifold.