The closest you can book a hotel is 0 mi. from Denali in Take a look on the Map
A little about Denali...
The word "Denali" means "the High One" in the native Athabaskan language and refers to the mountain itself. The mountain was named after president William McKinley of Ohio in 1897 by local prospector William A. Dickey, although McKinley had no connection with the region.
Charles Sheldon took an interest in the Dall sheep native to the region, and became concerned that human encroachment may threaten the species. After his 1907-1908 visit, he petitioned the people of Alaska and Congress to create a preserve for the sheep. The park was established as Mount McKinley National Park on February 26, 1917. Ironically, only a portion of Mount McKinley (not even including the summit) was within the original park boundary. The park was designated an international biosphere reserve in 1976. A separate Denali National Monument was proclaimed by Jimmy Carter on December 1, 1978.
Mount McKinley National Park, whose name had been subject to local criticism from the onset, and Denali National Monument were incorporated and established into Denali National Park and Preserve by the Alaska National Interest Lands Conservation Act, December 2, 1980. At this time the Alaska Board of Geographic Names changed the name of the mountain back to "Denali," even though the U.S. Board of Geographic Names maintains "McKinley". Alaskans tend to use "Denali" and rely on context to distinguish between the park and the mountain. The size of the national park is 4,740,906.73 acres (19,185.78 km²), of which 4,724,735.16 acres are federally owned. The national preserve is 1,334,200 acres (543.09 km²), of which 1,304,132 acres are federally owned. On December 2, 1980, a 2,146,580 acre Denali Wilderness was established within the park.
Denali habitat is a mix of forest at the lowest elevations, including deciduous taiga. The preserve is also home to tundra at middle elevations, and glaciers, rock, and snow at the highest elevations. Today, the park hosts more than 400,000 visitors who enjoy wildlife viewing, mountaineering, and backpacking. Wintertime recreation includes dog-sledding, cross-country skiing, and snowmobiling where allowed.