In the sleek restaurant of a boutique hotel a few blocks from the Cort Theatre, the Broadway house where her name is emblazoned on the marquee, Lydia Diamond looked over the breakfast menu with a careful eye on cost. “It’s a Pavlovian response to hotel prices,’’ she said. “And I spend so much time in hotels, it just makes me crazy.’’ Diamond travels a lot as a playwright. Lately she has been shuttling between New York, where her comedy “Stick Fly’’ began previews Friday, and Cambridge, where she lives.