The National Park Service has some terrific maps of Mt. Rainier NP, and while some of them are easily available on their Website, see Web page of map resources, some of them are not so readily apparent and take time to find where the respective Web pages are buried in the NP Website.
You can use the NPS search tool on the Mt. Rainier NP Website to find maps, but what you get is a list of the individual maps with some other links, but not the other maps available for different uses. The sad reality is that I found many of the Web pages for maps of Mt. Rainier to be incomplete or development pages with minimal information.
But that said, some map resources are listed below.
The first is a really cool one, their NP Map Viewer for Mt. Rainier NP. I can't find the Web page for any description or the traditional "wrapper" page which embeds this viewer. I'd appreciate help there if you know it or come across it.
The second is the NPS Harper's Ferry map server for other formats and maps.
The third are the NPS trail maps for 50 trials based on 2009 information. These are useful but don't provide downloadable or printable maps or print version of the Web page. They'd be really cool in a PDF file to put on tablets or cellphones.
The last aren't NPS resources but other Websites. One is the USGS Cascades Volcano Observatory Web page for Mt Rainier with maps and other resources.
Another is mine which offers the latest USGS 1:24,000 topographic maps as PDF files to download. I've loaded mine on to an iPad using GoodReader for the iPad.