The Fortezza da Basso is the building Florence likes least to talk about: a vast brick pentagon the Medici threw up in the 1530s with its guns pointed not outward at invaders but inward, at the citizens. It's a monument to control, and walking its sloped walls you feel the menace it was built to project.
About three kilometres, good in the afternoon. Start outside, at the base of a bastion, where the sheer mass does the talking. The Sangallo keep still stands at the core — you can usually walk the grounds between fairs, so check the day before. Inside, the ramparts now wrap glass-and-steel exhibition halls that host the Pitti shows and the artisan fairs: Renaissance walls, trade-fair lighting, a genuinely odd pairing.
Cross Viale Filippo Strozzi for the full scale of the thing, then walk south through the unglamorous working streets behind the station — repair shops and canteens, the city's back-of-house. Land at Michelucci's 1934 Santa Maria Novella station, a piece of clean Rationalist design most people rush straight past. Give it a look before you board.