The Polonsky Shakespeare Center, the new theater for the celebrated Theatre for a New Audience company, had its grand opening yesterday. Julie Taymor’s production of A Midsummer Night’s Dream, her first work since that whole Spider-Man thing, will play there until January. The Polonsky Center, on Ashland Place, the block between BAM’s two major theaters, is the first theater dedicated to classical drama to open in the city in a generation—and a keystone in the expanding BAM Cultural District, a few square blocks in Fort Greene on the Boerum Hill/Downtown Brooklyn borders that has become the borough’s arts capital. Many theater groups and other cultural organizations house their offices in the area, and several actual theaters—where you can see dance, plays, movies, art and more—are there, too. Here’s a guide to what you can see where.