On our first visit, the only place visited on the left bank was Piazza Michelangelo, which offers the classic and best view of Florence. This time, we spent the night a stone's throw from the piazza, in this house.
I can give you a link to the apartment (booking.com), but it are rarely rented, so it's not certain that they will be available. However, if you manage to book, you will have probably the best view in all of Florence.
The two main places that interested us on the left bank were the Boboli Gardens and the Bardini Garden. You can buy a ticket to Boboli Gardens online https://www.uffizi.it/en/tickets. It also gives you the right to enter Villa Bardini's garden.
The Boboli Gardens are quite large, here https://www.uffizi.it/en/boboli-garden#map you can download a map in PDF and see the entrances. We entered through the main entrance at the Pitti Palace (43.765420, 11.249850).
There is a gate between the Boboli and Bardini Gardens, here 43.764084, 11.253482. The only problem is that the gate doesn't always open, so sometimes you have to make a 1 kilometer detour. The entrance to Villa Bardini is here 43.763955, 11.255965.
The main route from the right bank to Palazzo Pitti goes across the Ponte Vecchio, but from Piazza Michelangelo you can walk along the promenade, which offers beautiful views of the Arno River and the magnificent palazzo of the right bank.
We also planned to visit Vasari's secret corridor, shown in the movie Inferno (2016). It runs from the Palazzo Pitti to the Palazzo Vecchio, inside the buildings and even inside the bridge. In 2021, however, it was still closed. Check this page for updates https://www.uffizi.it/en/corridoio-vasariano.
The Boboli Gardens is an outstanding horticultural ensemble of the second half of the 16th century. The name comes from the first owner of this land, but the gardens themselves were laid out by the great dukes of Tuscany, the Medici. The Pitti Palace is their main residence.
Inferno (2016) was also filmed in Boboli Gardens, where the adventures of Professor Langdon with another young companion began. If you are searching for the staircase and the door, then they are here 43.766041, 11.251914.
The Bardini Garden is much smaller, the entrance and exit are in different places, you go down the slope. The gardens are laid out on the site of former vineyards, the area belonged to the Mozzi family from the thirteenth to the sixteenth century. After the family went bankrupt, the gardens changed hands and were rebuilt many times. Because of this, during the descent, you will visit at least three different gardens created in different time periods.
The garden is famous for its excellent views of the city and its large baroque staircase.