Solo, Palazzo Vecchio works.
Two experiences worth the ticket, both about standing inside power. The Salone dei Cinquecento is staggering in person — a vast hall where Vasari's wall-to-ceiling battle frescoes loom over you while the building still works as the functioning city hall, clerks crossing the courtyard below. The Secret Passages tour is the sleeper: a guide takes you up hidden stairs inside the walls, through the roof trusses above that painted ceiling, and into the tiny studiolo where Francesco I hid his treasures — genuinely thrilling, and the most fun thing a kid can do in central Florence. The catch is splintered ticketing (museum / tower / archaeology / passages all separate), and the free statue gallery outside is so good some skip the paid interior entirely.