The State Department spent $52,701 last year buying customized and mechanized curtains for the picture windows in Nikki R. Haley’s official residence as ambassador to the United Nations, just as the department was undergoing deep budget cuts and had frozen hiring. The residence, in a new building on First Avenue, has spectacular views, and Ms. Haley is the first ambassador to live in it. For decades, her predecessors lived in the Waldorf Astoria hotel. But after the hotel was purchased by a Chinese insurance company with a murky ownership structure, the State Department decided in 2016 to find a new home for its top New York diplomat because of security concerns. The government leased the apartment, just blocks from the delegation’s offices, with an option to buy, according to Patrick Kennedy, the top management official at the State Department during the Obama administration. The full-floor penthouse, with handsome hardwood floors covering large open spaces stretching nearly 6,000 square feet, was listed at $58,000 a month.