In addition, though the centro storico has more artistic treasures per square metre than any other city in the world, Florence also has many more low-key charms. Take time to read between the lines by visiting its dozens of lesser-known museums, and stopping by its hundreds of historic churches. You could spend days just taking your time exploring its back streets and quieter piazzas, and seeking out local trattorias and bars.

Central Florence is dominated by the splendid piazza del Duomo, and, at its core, the Duomo (055 230 2885), the city’s cathedral, its exterior inlaid with intricately patterned pink, white and green marble. It soars above the surrounding buildings; in fact, it’s so huge that there’s no point nearby from which you can see the entire building, although you’ll get tantalising glimpses wandering through the neighbouring streets. Brunelleschi’s massive cupola, an extraordinary feat of 15th-century engineering, adorns the eastern end of the building. Climb up into the dome for a bird’s-eye view, inside and out, or head instead to Giotto’s adjacent belltower (055 230 2885). Built in 1334, it offers extraordinary views.

Directly west of the Duomo, the small, curved Baptistery dates back to 1059. Its elaborate bronze doors tell Biblical tales, as does the intricately painted dome inside. It’s very near the bijou Museo di Bigallo (piazza San Giovanni 6, 055 215 440, closed Tues), in a beautiful loggia with gorgeous frescoes of 14th-century Florence in exquisitely painted detail. On the north side of the Duomo, the Museo dell’Opera del Duomo (via della Canonica 1, 055 230 2885) houses the many treasures once contained in and around the Duomo, including the tools used to build it, the original wood models of the cupola and sculptures deemed too precious and vulnerable to leave outside, such as the heart-rending Pietà Bandini by Michelangelo.

Of all its many squares, this is Florence’s showpiece piazza, with the 13th-century crenellated Palazzo Vecchio and copy of Michelangelo’s David, along with Donatello’s Marzocco and a few sexy nymphs and satyrs splashing in Ammanati’s over-the-top Neptune fountain.

Heading towards the river from the piazza Signoria, the piazzale degli Uffizi is home to the greatest museum of Renaissance art in the world, the Uffizi Gallery (055 238 8651 www.uffizi.firenze.it, closed Mon). Occupying the former offices of the Medici administration, many of Italy’s most celebrated paintings can be seen here – the Uffizi has a room filled with nothing but Botticellis, including the famous Birth of Venus and the glowing Allegory of Spring, along with stunning works by Michelangelo and Titian. In high season, it’s always a good idea to book a ticket in advance in order to avoid the museum’s notoriously long and slow-moving queues (to book tickets for all state museums in Florence, including the Uffizi, 055 294 883). Heading down towards the river from the Uffizi brings you to the whimsical Ponte Vecchio, which dates back to the 14th century. With its tiny jewellery shops that are perilously perched on a narrow river crossing, the Vecchio is one of the most photographed bridges in Europe.

This richly varied area around the train station offers the sublime and the sleazy, mixing lovely churches with the usual near-the-station grit. Its most civilised pleasures are near the fine Museo Marino Marini (piazza San Pancrazio, 055 219 432, closed Tue, Sat & Sun in summer, Tue & Sun in winter), with its excellent sculptures by Marino Marini (1901-80), and in the piazza Santa Maria Novella and the church of the same name (055 219 257), which holds Trinità by Masaccio (1427) and Giotto’s recently restored Crocifisso.

This student quarter buzzes with backpack-toting youths of international origin, but lures everybody else with one very significant nude. On the via Ricasoli corner of the piazza Annunziata, a never-ending queue lets you know you’ve found the Galleria dell’ Accademia (via Ricasoli 58-60, 055 238 8612, closed Mon), home to Michelangelo’s magnificent nude, David. Carved from a single massive lump of marble in 1504, he’s in fine form, sparkling from head to toe, as he’s just been cleaned.

Nearby, the unmissable Museo di San Marco (piazza San Marco 3, 055 238 8608) is one of Florence’s most serene museums and occupies the ex-convent of San Marco, where Fra Angelico once lived as a monk. He is arguably the most spiritual artist of the Renaissance era, and his ethereal paintings are the main attraction here.

The huge area that surrounds Santa Croce is one of Florence’s richest neighbourhoods in which to explore. On the western edge, across from the bulky Palazzo Vecchio, piazza San Firenze houses the sculpture-laden Bargello (via Pronconsolo 4, 055 238 8606). The ancient building was once a prison, but now contains some superb Renaissance sculpture, including Donatello’s Druids, Michelangelo’s androgynous Bacchus and Giambologna’s fleet- of-foot Mercury. Nearby, on piazza Santa Croce, the mock-Gothic church of Santa Croce (055 244 619) dates back to the 13th century, and is filled with the tombs of the city’s illustrious dead. Dante’s tomb is just a memorial, as he was buried in Ravenna, but Michelangelo does actually lie in his elaborate tomb, as does Galileo in his.

This district south of the river is where Florence’s modern artisans live and work, surrounded by the work of their forefathers. For a completely over-the-top glut of sensational painting, head to the gorgeous Galleria Palatina (piazza Pitti 1, 055 238 8614, closed Mon) inside the Pitti Palace, where the Medicis’ hoard hangs floor to ceiling in a series of lavishly decorated rooms; look out for Lippi, Raphael, Titian, Rubens and Perugino. In hot weather, the leafy glades, ornate fountains and hidden paths of the magical Boboli gardens (055 229 8732), laid out on the hill behind Pitti, are particularly inviting.

Heading west, past the Ponte Vecchio, the bohemian areas of Santo Spirito and San Frediano are named after their churches. Piazza Santo Spirito is lively, but low-key and very local, with lots of good, inexpensive trattorias and a produce market every morning, as well as a fleamarket on Sundays. In the summer, a huge bar is set up in the middle of the square and crowds relax on the steps of the remarkable church of Santo Spirito (055 210 030), with its perfectly proportioned nave by Brunelleschi.

South of the piazza, the narrow via Romana is lined with unusual crafts and antiques shops. By night piazza del Carmine fills up with crowds during the warmer months. It is home to the baroque Santa Maria del Carmine church, with the matchless 15th-century frescoes housed by the Brancacci chapel (piazza del Carmine, Museum Cappella Brancacci, 055 238 2195, closed Tue).

• Tourist information: via Cavour 1 (055 290 832, www.firenzeturismo.it).