By Tobias Carroll Jeff Klein, founder of JK Hotel Group, is best known for his work in Los Angeles, which includes the Sunset Towers as well as a private club, the San Vicente Bungalows. But the latest destination Klein has in mind for a members-only club can be found on a different coast. According to a report by Shawn McCreesh at Intelligencer, Klein has big plans for the Jane Hotel — plans which he’s dubbed “SVB NYC.” Which, you’ll have to admit, is pretty catchy. This won’t be the first time Klein’s worked on a project in New York City. Among other things, he and Graydon Carter were partne…