This secluded beach off Rte 82 offers no shade or facilities, and you'll have to hike about 20 minutes through scrub to reach it, but you'd be hard-pressed to find a more beautiful stretch of sand. The Nature Conservancy manages the area as part of a preserve for green and hawksbill turtles, which are active from July to December. Snorkeling on the coral reef here is good, though be careful of the strong current.
To get to the beach, take the trail down the hill from the Point Udall car park. Isaac Bay is actually the second beach you come to on the trail (down the wooden stairs). From the western end of Isaac the trail continues to Jack Bay, which is also part of the nature preserve. Nudists sometimes hang out on the beaches.