One of the best ways to spend a lazy afternoon climbing in Jackson, swim or paddle out to the island and enjoy some scenic toproping.
Scramble on top of the main boulder from the east side and set up your climbs off of several bolts on the west and northwest sides. There are a few cracks on top of the boulder that would be possible (with some creativity) to rig anchors from. Many excellent climbs from around 10- to 11+ are possible.
Note: As of Sep 2009, the pair of bolts off the northwest side were 1/4 inchers & rusted. Other set was solid
From the Leigh Lake parking area, follow the trail north towards Leigh Lake. After approximately 3/4 of a mile, follow signs toward the Leigh Lake Portage. From the shore of the lake, swim to the island approximately 50 yards away. The island is also quite clearly marked on the USGS topo.
Alternatively, launch a canoe/sea kayak from the same trailhead and paddle north on String Lake until you are forced to portage your boat ~200 yards to Leigh Lake. Paddle across to the same island...but why would you bother with that? Just carry a pool toy if you can't swim.