The Forest Service maintains two summer-only campgrounds in the Juneau [1] area, but neither is close to town. Hugging the shore of Mendenhall Lake, Mendenhall Lake Campground (www.recreation.gov [2] for reservations) has glacier views and access to several hiking trails. You will find backpacker units and vehicle sites ($10) along with RV sites with full hookups ($26–28). From the ferry terminal, turn right and go two miles to De Hart’s Store, then left onto Loop Road. Follow it three miles to Montana Creek Road, then another 0.75 miles to the campground.
Auke Village Campground ($10) is 16 miles north on Glacier Highway [3] and another two miles out on Point Louisa. The area is secluded, with a nice beach and views of nearby islands. If you lack a vehicle, the nearest city bus stop is four miles away.
Eagle Beach State Recreation Area (Mile 28, 907/586-2506, mid-May–mid-Sept., $10) has rustic campsites (no water). Nearby is a picnic area with all-encompassing views of the Chilkat Range.
The city of Juneau [1] has four RV spaces at Savikko Park (907/586-5255) on Douglas Island. They are free, but there are no hookups, tents are not permitted, and stays are limited to three days.
Auke Bay RV Park (907/789-9467, year-round, $26 full hookups, no tents) is 1.5 miles southeast of the ferry terminal. Reservations are recommended.
Spruce Meadow RV Park (10200 Back Loop Rd., 907/789-1990, www.juneaurv.com [4], year-round, $32 RVs, $20 tents) is four miles from the ferry terminal. In addition, RVs can generally overnight at Nugget Mall near the airport for free, but there are no facilities, of course.
Links:
[1] http://www.moon.com/destinations/alaska/southeast-alaska/juneau
[2] http://www.recreation.gov
[3] http://www.moon.com/destinations/alaska/southeast-alaska/juneau/sights/glacier-highway
[4] http://www.juneaurv.com