There are two inns within the park itself; both are run by the park concessionaire, Mount Rainier Guest Services (360/569-2275, www.mtrainierguestservices.com [1]). Each has a storied history and offers unparalleled access to the park, but for real comfort and relaxation the cabins and B&Bs in Ashford [2] really are the way to go.
Prices at both inns within the park are through the roof, and neither can quite shake that bit of institutionalized dreariness that lingers around many lodges within the national park system.
The National Park Inn ($107–197 s or d) at Longmire [3] is open daily year-round. This inn has a central stone fireplace and decent rooms with shared or private baths.
Built in 1917, Paradise Inn ($99–228 s or d) is an imposing wooden lodge with high ceilings, stone fireplaces, and unsurpassed mountain views from its elevation of 5,400 feet. The lodge underwent a $22 million renovation in 2008, but even after that the units are still not exactly up to luxury levels. The lodge is open daily from late May through September; rooms have shared or private baths.
Links:
[1] http://www.mtrainierguestservices.com
[2] http://www.moon.com/destinations/washington/south-cascades/ashford
[3] http://www.moon.com/destinations/washington/south-cascades/mount-rainier-national-park/sights/longmire-area