There's a lot more to this park than beautiful petrified wood. Start your visit at the Painted Desert Visitor Center. There is a film, exhibits, and a short interpretive loop trail. You'll also find the Painted Desert Inn National Historic Landmark, a resting place for early route 66 travelers. At nearby Kachina Point, the 1-mile round trip Painted Desert Rim Trail offers the best views of the colorful Painted Desert. This is as much of an attraction here as the petrified wood. Horseback riding is available in the area, but for those with cars or bikes, head down the main park road for 28 miles of colorful viewpoints.
To the south is the short .3-mile loop called Puerco Pueblo. This brings you to ancestral Pueblo remains. Nearby Newspaper Rock has petroglyphs. Further south is a turnout for the Blue Mesa area. The Blue Mesa 1-mile loop gives you a look at sedimentary badlands. Billings Gap is a longer 3-mile hike in this area. Head further south to Jasper Forest area for two more great hikes. First Forest Point is a 2.1-mile round trip through petrified wood and giant boulders. The Jasper Forest Hike is a 2.5-mile round trip into a dense patch of petrified wood that was popular with early tourists.
At the southern end of the park road, you'll come to the Rainbow Forest area. The Rainbow Forest Museum and Visitor Center. It features skeletal displays of prehistoric animals. The museum's Blue Mesa Room has a profound display on the geologic history of the region. There are three good hikes here that I strongly recommend. The Giant Logs .4-mile loop has some of the largest logs in the park, including one that is about 10-feet wide! The colors here are astounding. The Long Logs 1.6-mile loop brings you by a large gathering of petrified logs. Agate House is a 2-mile round trip to see a 700-year-old Pueblo home built with the petrified wood. There's a way to combine Long Logs and Agate House trails that will shave a mile off the round trip total.
The only camping in the park is backcountry camping via permit. But there is lodging in neighboring towns, which gives you an excuse to traverse the historic route 66. You'll notice a lot of old buildings, signs, and overgrowth along the way that makes for unique photo opportunities.