Trattoria Cibreo
Via dei Macci, 122r, 50122 Firenze
One of the best places where to try the typical Tuscan cuisine. It is a very traditional Italian restaurant that is worth a stop.

Mercato di San Lorenzo
50123 Firenze FI
Florence’s central market, it is actually divided in 2 parts: the indoor part is known as Mercato Centrale (“Central Market”) and is more focused on food, the outdoor area which extends in the surrounding streets is known as Mercato di San Lorenzo and mostly sells leather goods (typical of the region), clothes and many other souvenirs.

SandwiChic
Via S. Gallo, 3r, 50129 Firenze FI
One of the best places to have a sandwich with some of the best cured meat. It is a small place and often full of people, but waiting a little to try one of their sandwiches is worthwhile.

What can't be missed:

Chiesa di San Miniato
Via delle Porte Sante, 34, 50125 Firenze
Near the Parking Michelangelo, this is one of the highest spots in the city from which to see Firenze. It is also one of the best examples of the architectural style known as ‘romanico fiorentino’ (which can be found only in this particular area of Italy as it historically developed only here).

Chiesa Ognissanti
Borgo Ognissanti, 42, 50123 Firenze
Here you can see art pieces from the 1400s and 1500s.

Giardini di Boboli
Piazza Pitti, 1, 50125 Firenze
This historical park was intended to be a garden to the Pitti Palace and it is one of the most important examples of italian garden. It is literally an outdoor museum both from an architectural point of view and from a sculptural one.

Vasariano Corridor  
Lungarno degli Archibusieri, 2, 50122 Firenze
An elevated route which connects Palazzo Vecchio with Palazzo Pitti passing through the Uffizi and over Ponte Vecchio. It is currently considered part of the Uffizi where it starts and it ends at Giardino di Boboli. It holds one of the largest collections of self portraits and portraits of the ‘600s and ‘700s.
[you’ll have to check if there are guided visits when you go and book it beforehand: Uffizi.com]