In the groves where the nymph Egeria once laid down the law for Numa Pompilius, big bands now lay down the groove for rug-cutting Romans. One of the city’s most treasured and least touristed public parks, the gardens of the 16th-century Villa Celimontana blossom each summer with jazz—including Swing Swing Swing, in which Jitterbug and Lindy Hop lessons are followed by dancing to live big bands. —E.E.