Monument Valley is the best place to see scenic southwest landscapes. The valley is famous for movie settings, and is a favorite place for photographers. Monument Valley lies at the northernmost part of Arizona by the Utah border. It really is in the middle of nowhere. It takes about 4-5 hours drive from Phoenix, Las Vegas or Salt Lake City, but it's worth the trip as you can combine visits with other national parks, such as Arches National Park or the Grand Canyon.
Many people traveling along Highway 163 in Arizona and Utah will see the massive buttes and spires in the distance, and may not think it's worthwhile to go into the park. However, the best views lie within this park, which is on Navajo tribal land.
Be sure to drive all the way to Totem Pole which is about 5 miles from the entrance. Along the way, you will see the Three Sisters rock formation and another great lookout from Artist Point. The roads in the park are unpaved, but still accessible by rental car. These photos were taken a day after a winter storm, so the roads had some minor flooding, but at least they weren't dusty.
If you want to see more of the backcountry, you can do it by horseback. There is a very friendly Navajo operator within the park offering guided horseback tours.