Here's an ideal itinerary for 4 days in Firenze:

Day 1:

• Start your day with a visit to the iconic Duomo di Firenze, also known as the Florence Cathedral. Climb to the top of the dome for breathtaking views of the city.
• Next, head to the Uffizi Gallery, one of the most famous art museums in the world. Marvel at works by Botticelli, Michelangelo, and Leonardo da Vinci.
• For lunch, try some authentic Tuscan cuisine at Trattoria Mario, a local favorite.
• In the afternoon, take a stroll through the Boboli Gardens, a beautiful park filled with sculptures, fountains, and stunning views of the city.
• End your day with a visit to Piazzale Michelangelo, a hilltop square with panoramic views of Florence.

Day 2:

• Start your day with a visit to the Accademia Gallery, home to Michelangelo's famous sculpture, David.
• Next, head to the Mercato Centrale, a bustling indoor market filled with fresh produce, meats, cheeses, and more. Grab some lunch here and enjoy the lively atmosphere.
• In the afternoon, take a walk across the Ponte Vecchio, a historic bridge lined with jewelry shops.
• End your day with a visit to the Palazzo Pitti, a grand palace filled with art and history.

Day 3:

• Start your day with a visit to the Basilica di Santa Croce, a beautiful church filled with art and history.
• Next, head to the San Lorenzo Market, a bustling outdoor market filled with leather goods, souvenirs, and more. Grab some lunch here and enjoy the lively atmosphere.
• In the afternoon, take a walk through the Oltrarno neighborhood, a charming area filled with artisan shops and local cafes.
• End your day with a visit to the Piazza della Signoria, a historic square filled with sculptures and beautiful architecture.

Day 4:

• Start your day with a visit to the Palazzo Vecchio, a grand palace filled with art and history.
• Next, head to the Museo Galileo, a fascinating museum dedicated to the history of science and technology.
• For lunch, try some delicious pizza at Gusta Pizza, a local favorite.
• In the afternoon, take a walk through the Giardino Bardini, a beautiful garden filled with sculptures and stunning views of the city.
• End your day with a visit to the Santa Maria Novella, a beautiful church filled with art and history.

I hope this itinerary helps you plan your trip to Firenze!