Kayenta itself is a small, walkable cluster of motels, restaurants, and a supermarket. Everything you need is within a short drive of US-163.
Monument Valley Navajo Tribal Park is 25 miles north on US-163. The park entrance road leads to the visitor centre, where you can pay your admission fee (currently around $20 per vehicle) and attempt the 17-mile unpaved Valley Drive loop. This loop requires a high-clearance vehicle — it is deeply rutted in places and rental car companies typically prohibit their vehicles on unpaved roads. The wiser choice is a Navajo-guided jeep tour, which also gets you to parts of the valley closed to independent travellers.
Beyond Monument Valley, Navajo Nation roads vary from smooth tarmac to rough dirt tracks. A four-wheel-drive vehicle is useful if you plan to explore off the main highways. Always carry water and let someone know your itinerary.