Staying in a wilderness lodge makes for a completely different experience of Denali, and that's why I've segregated these choices here. These lodges are self-contained vacations, and if you choose to stay you don't need to worry about the shuttle bus or the other issues of escaping the "frontcountry." The lodges also are expensive and require a significant commitment of time. It doesn't make sense to spend less than 3 days, and some lodges require longer minimum stays.
All lodges within Denali National Park are in the Kantishna district, an inholding of private land where gold miners staked claims before the park was created. The lodge operators who later obtained this land gained something more valuable than gold: the opportunity to bring visitors to the far end of the park from the entrance, as near as a vehicle can get to Mount McKinley, without using the park's shuttle system. Hosts drive visitors to Kantishna in their own buses or vans over the 91-mile park road. These lodges are open only in summer.
I also recommend Denali Backcountry Lodge (tel. 877/233-6254 or 907/376-1992; www.denalilodge.com).