An excellent free campground at Bartlett Cove comes complete with bear-proof food storage caches, outhouses, and a three-sided shelter with a woodstove (great for drying your gear after a kayak trip up the bay). The campground is only 0.5 miles from Glacier Bay Lodge and usually has space. Running water is available next to the backcountry office.
All cooking must be done below the high-tide line (where the odors are washed away every six hours) to reduce the chance of bear problems. You can store things for free in the shed next to the backcountry office.
No trails exist anywhere in Glacier Bay [1]’s backcountry, but Park Service rangers can provide details on hiking and camping up the bay. Camping is allowed in most park areas. Exceptions are the Marble Islands—closed because of their importance to nesting seabirds—and a few other areas closed because of the potential for bear incidents. A gas stove is a necessity for camping, since wood is often unavailable.
Free permits (available at the backcountry office) are recommended before you head out. Park naturalists provide camper orientations each evening, including information on how and where to go, bear safety, and minimum-impact camping procedures. Bears have killed two people within the park in the past decade or so, and to lessen the chance of this happening, free bear-proof containers are loaned to all kayakers and hikers. A small storage shed beside the backcountry office is a good place to store unneeded gear while you’re up the bay. Firearms are not allowed in Glacier Bay.
Links:
[1] http://www.moon.com/destinations/alaska/southeast-alaska/glacier-bay-national-park