Monument Valley is about 121 miles from Page, which makes for a solid day trip. There are a few hotels at Monument Valley, or you could get a hotel in Kayenta, which is only 21 miles from Monument Valley or Mexican Hat, which is also about 20 miles away. There just a few hotels to choose from in these areas as they are all located in the Navajo Nation. That goes for food and ammenities as well. For more Monument Valley hotel choices, dining options, groceries and other ammenities, you'll want to make Page your home base.
If you're thinking about camping in Monument Valley, it can certainly be an experience to remember especially if you take a more "off-the-beaten-path" approach. They are a few really nice, established campsites, such as The View campground attached to The View Hotel and a KOA, both of which have RV sites with hookups. But if you can camp without amenities, there are several private, Native American landowners who will host you. Try camping at some lesser-known campgrounds such as Holiday Tribal Park campsite. Hosts are known to offer guiding services as you'll need one to get around since much of the land is private and roads are unmarked. Knowing somebody or hiring a guide is a great way to experience the real Southwest.
Backcountry Permits for Hiking and Camping
Backcountry permist are required for hiking and camping on designated trails and campgrounds within Monument Valley Park. If you are caught hiking or camping in the park without a Backcountry Permit, or in unauthorized territory, additional fees will apply. The purchase of a Backcountry Permit is in addition to the general admission fee. The Navajo Nation is comprised of more than 25,000 sq. miles and offers hikers numerous isolated trails and routes, so permits are issued for the safety of hikers who enter the reservation and for the protection of natural and cultural resources. Here is more Monument Valley Backcountry Permit for camping and hiking information.