Reading through earlier reviews a few concerns jumped out: the road in is a decent gravel road, but side roads often require 4x4 and may not be suitable for trailers.
The rough drive is intentional, to keep out too much traffic for Navajo who live nearby. Please do remember you're on another people's homeland, and treat all interactions with respect, like a polite guest should.
Most park staff are local hires from the Navajo Reservation, which surrounds the park. They'll be some bilagaana (white) rangers too, most likely LEOs and any archeology staff. The astro-archeology park staff talks by the telescope are well worth it, and show how the ruins line up with canyon walls and celestial phenomenon.
Chaco is a dark skies park, so night sky gazing is fantastic on clear nights when the moon isn't shining.
There are ruins right in the campground and you can hike to other ruins directly from camp as well. I've found a bicycle the perfect way to get around as the whole park loop is too far to easily walk and traffic slow, with parking sometimes limited at peak times.
Chaco is one of the few archeological parks where one can easily access amazing monumental architecture: in nearby Mesa Verde most sites are off limits or require ranger guided tours.
For those who are interested in learning about Ancestral Puebloan cultures, this is literally a sacred site. Indigenous people, the descendants of Chaco's creators, still live nearby and make use of Chaco today for ceremonies. The place deserves respect from all who visit.
Fall is the best time to visit, combining the golden cottonwoods and bright yellow Aspen foliage with cool nights for easier sleep and no bugs. Spring works too, but can be windy, with winters being sometimes frigid and summers often broiling.
Off season makes scoring a spot easier as well, and even winter will have reasonable camping temperatures some weeks.