The teeming hordes of tourists who descend on Manhattan in the summer rarely stray far from Times Square in search of theater. But there is plenty of stage activity in the other boroughs too. A whimsical riff on ”Hamlet” opens this week at an appropriately unusual site, the McCarren Park Pool in scruffy-hip Brooklyn. ”Twelve Ophelias,” by Caridad Svich, imagines an afterlife for Elsinore’s unluckiest lass. Ophelia pops out of the water, squeeze-dries her skirt, tosses aside the water-logged flowers and sets out for new adventures in a new world. Elsinore, you see, looks a lot like Appalachia in this twisted take on the tragedy. A bluegrass band, the Jones Street Boys, supplies an original score for this production from the Woodshed Collective, founded by Vassar alumni.