Catty-corner from the downtown Wortham Center, the Houston Ballet is planning a new, $53 million home. It will house its offices, rehearsal space and the Ben Stevenson Academy, the ballet’s educational wing, named for its long-time artistic director — who is now the head of the Texas Ballet Theater. Plans call for a skywalk to connect the building with the city-owned Wortham, where the Houston Ballet presents six programs a year, plus a month-long run of The Nutcracker.