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You sure look comfortable up there!
The Tablelands are around 16 or so miles due west from Whitney -- great area, and no trails, so very few people ever visit it. See my picture of an unnamed little lake at 11,200 feet. (Tom Harrison's Mt. Whitney High Country Trail Map is a great topo of that whole area, and it's part of his JMT topo pack, too.)
Hey, if you get a sudden urge to complete a W. day-hike this week/end, we can rideshare. I think I'll need to squeeze in one more before the close of the Sierra hiking season!