Florence's best park is the Medici grand dukes' old backyard to the Pitti Palace, the Giardino di Boboli. Less scenic, but free and more jogger-friendly, is the Parco delle Cascine along the Arno at the west end of the historic center. Originally a wild delta of land where the Arno and Mugnone rivers met, the area later became a Medici hunting reserve and eventually a pasture for the grand duke's milk cows. Today, the Cascine is home to tennis courts, pools, a horse racetrack, and some odd late-18th- and early-19th-century features like an incongruous pyramid and funky neoclassical fountains. There's a flea market here every Tuesday morning. Although perfectly safe in the daylight, this park becomes a hangout for drug addicts after dark, as do many sections of the Arno's banks away from the center, so steer clear.
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