Sadly, the Painted Forest Inn in the national park stopped renting out rooms long ago (in 1963). The nearest motel rooms to the park are in Holbrook, some 21 miles to the west along Interstate 40.
Perhaps one reason folks don't spend more time exploring the park is that lodging is not readily available.
Holbrook doesn't exactly act much like a gateway town—one restaurant stopped serving dinners at 9 p.m.—but you'll find plenty of rooms to rent, mostly in namebrand roadside establishments.
The eastern end of town just off the interstate offers a good handful of motels—Motel 6, Days Inn, Econolodge, among others. For a complete listing, check out this site.