There area lot of campgrounds in the area around Mountain Home. The two closest to the range are the Bull Shoals - White River state park and Lakeview Park (COE), both in Lakeview, AR.
Mountain Home offers a wide range of motels. A Google search for "Mountain Home AR motels” gives a pretty complete list.
The Mountain Home Chamber of Commerace also has a pretty complete list, including other things to do and see in the area.