We traveled in the Southwest with our three children ages 2, 4 and 6 for 10 days. We have been to Albuquerque, Petrified Forest, Sedona, Sunset Crater, Grand Canyon, Monument Park, and Canyon de Chelly.
We got there by airplane. We had two suitcases for five people and five pieces of carry-on. That was a mistake: nobody cared for books, sandwiches and spare clothes for everyone on the flight. Next time I'll pack everything in the luggage. We rented a minivan in Albuquerque airport. Southwest is a vast, rather poor by American standard, and sparsely populated place; it's worth mentioning that the average elevation is 3500 ft. It takes time to get used to climate most vacationers don't have. Drives are long and attractions, gas stations, repair shops, and fast food joints are far between. Refuel when you can and carry your food and water with you. We had GPS and a portable ham radio as well.
Around Albuquerque: Petroglyph National Park is almost within city limits. It has several short (0.2-0.5mi) trails accessible for a 4-year old. It's considerably colder and windier in the park than lower in the Rio Grande Valley. Sandia Peak tramway is 3 miles long -- claims to be the longest in the world. It brings you up to the top, which is worth the walk even off the skiing season, and the view of the valley is spectacular. Santa Fe is about an hour's drive from Albuquerque. It's artsy, with several blocks of old Mission buildings and narrow streets. Albuquerque has its own Zoo, science museum, and an annual hot-air baloon festival. I highly recommend the privately owned Rattlesnake Museum. It's a small terrarium with a gift shop. They have several dozens of different rattlesnakes, turtles, lizards, and tarantulas; one hour will be just right for the place.
On the way to Grand Canyon: 4 hours to Petrified Forest/Painted Desert National Park via I-40. You can camp there, but need to get to the park before dark (5PM October-March, check with the park service) to obtain the camping permit. The park is worth every second you spend there. Even if you don't get out of the car, the park road spans the park between I-40 and AZ-180 which will bring you back to interstate in Hollbrook further north. We stayed the night in La Posada hotel in Winslow 35 miles west. It is an old restored hotel from the extinct Harvey's chain. Used to be a railroad hotel.
Winslow to Flagstaff: one hour. The road climbs higher, pines and maples replace grass and cacti. AZ-89 goes down to Sedona along the Oak Creek (another hour). Further south is Montezuma Castle National Monument. An hour drive and about an hour to spent there.
We drove back north to get to the Sunset Crater. It has several one-mile trails, no lodging or campgrounds. A half-day project. The walks are easy and some are stroller accessible. Real black lava of different sorts, pines and juniper. No volcanic activity. Kids kept talking about the real volcano for month after the trip.
Grand Canyon: The National Park is surrounded by reservations. They offer tours, boats, lodging and such we didn't try. There are four hotels in the park itself on the south rim of the canyon. Northern rim is unaccessible in winter. There are view points along the rim and a rim trail. The rim trail is easy, but scary, with no fences for the most part. There is also a trail down, to the bottom of Canyon, we didn't risk with small children. The IMAX Theater in Tusayan runs the Grand Canyon documentary with effective imitation of rafting, flying over the Canyon and climbing it's walls.
On the way back we took AZ-64 to AZ-160 to Kayenta and returned to I-40 by AZ-191. It took us two days, and we saw the Monument Valley and Canyon de Chelly, both are Tribal Park. All in all, it was a mistake: the eroded rocks were not as impressive after the Grand Canyon, Sedona and the Painted Desert, and we had no use for the tribal trinkets. We had better spend another day at Grand Canyon.
See also: children, travel with kids.