Reliably Good Time!
I visit Stuart Island several times a summer. It's an easy paddle from Roche Harbor and the island I work on. There are eight-ish campsites on either side of the beach at the very end of Reid Harbor. Each side of the beach has a composting toilet. Up a steep set of stairs there is another set of campsites that connect over to Prevost Harbor. Be warned that the campsites fill up fast during the high season.
The best part of camping on Stuart Island is the walk up to the Turn Point Lighthouse. Along the way you can visit a small museum, the island's library, and an old one room schoolhouse. You also walk through damp forests, by an airstrip, and through farmland. Orca frequently pass by Turn Point so maybe you'll get lucky! The views over to Canada are gorgeous at sunset.