There's an addit (opening to a mine) off of the trail/road between the Carbon River entrance and Ipsut Creek campground. The trail is perhaps a mile from the ranger station, on the side of the main trail/road, away from the river.

The trail is steep, but short (only 0.25 miles each way).

The addit is covered with an iron gate 5 or so feet into the mine. Rails and ties are visible.

http://www.nps.gov/history/history/online_books/mora/hrs.pdf

Washington Milling and Mining Co ... http://www.ghosttownsofwashington.com/Mt.html

http://www.nps.gov/history/history/online_books/mora/hrs.pdf -- page 114

http://books.google.com/books?id=xv4qlIPaSLUC&pg=PR9&lpg=PR9&dq=washington+milling+and+mining+company+mount+rainier&source=bl&ots=mDKXmI_cXo&sig=lDhU7LRXVZ8Pu8I2mp4HDrqQ_Sw&hl=en&sa=X&ei=34FxT83XE43aiQKxq4neDA&ved=0CE8Q6AEwBQ#v=onepage&q=washington%20milling%20and%20mining%20company%20mount%20rainier&f=false

Pictures

following text from

Mount Rainier: A Visitor's Companion

By George Wuerthner, Douglas W. Moore

c 2000 Stackpole books

pg 23-24

Though most of the claims were never developed, a few mining operations did persist in the park for years. In Glacier Basin, the Mount Rainier Mining Company constructed a sawmill, power plant hotel, and other buildings. Ruins of this operation still exist. A second major attempt at developing a mine occurred on Eagle Peak. Between 1914 and 1930, buildings and tunnels were constructed on the site. A flume was built to carry water to a powerhouse near the Paradise River. The remains are still visible today.

Remains of old mining shafts, rusted tools, pipes and buildings are visible in other parts of the park, including the sites of the Washington Mining and Milling Company and the Hephizibah Mining Company development, both along the Carbon River, and at the North Mowich Glacier Mine. In most cases, nature has largely reclaimed these sites.