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I found a few..
Secret Archives, The entrance to the Archives, adjacent to the Vatican Library, is through the Porta di S. Anna in via di Porta Angelica (rione of Borgo). The translation of "Archivum Secretum Apostolicum Vaticanum" doesn't mean secret, but more accurately means the Pope's Private Library. Created in the 1700's, closed to outsiders until 1881, when Pope Leo XIII opened them to researchers, more than a thousand of whom now examine some of its documents each year. Still Parts of the Secret Archives remain truly secret, some materials are still prohibited for outside viewing, including everything dated after 1939.
Tower of the Winds, the Vatican's first astronomy tower. The 200-foot-high structure was built in 1578 so that the pope's astronomers could track the movements of the sun and stars and record the shifting directions of the wind. Because access is only through the Vatican Secret Archives, very few outsiders get to set foot in there. This one perhaps is not so secret, but hidden, or lesser known due to it's location. Inside is a fresco of St Paul's shipwreck on Malta. only St. Peter's Basilica stands higher than the tower. On the wall is a coin-size hole , every March 21, a ray of sunlight points to noon on an eight-pointed rosette in the floor to mark the spring equinox.