Apartment near Duomo in Florence

To live like a local get farther away from Duomo.
Look at the Santa Croce area.

Search on VRBO or AirBnB.
Everything in the historical center is near the Duomo. The historical center is only 500 hectares (less than 1250 acres or less than 2 square miles).
The Oltrarno area (on the south bank of the river) is cheaper, a bit less crowded with tourists, and more likely to have any Florentine residents left. Most of the historical center on the northern bank is now tourist or student rentals. The area of Santa Croce (eastern end of the historical center) is also less crowded with tourists.

We stayed in a two bedroom apartment overlooking Borgo San Lorenzo and it overlooked the street with restaurants, shops, etc. We enjoyed being a part of the bustle of the city. Steps from the Duomo.

https://www.airbnb.com/rooms/15119780?adults=1&children=0&infants=0&pets=0&check_in=2023-01-17&check_out=2023-01-22&source_impression_id=p3_1673923865_qhYfZsQOIV0TQ%2F1x

Via AirBnB, we stayed at a lovely apartment hosted by Chiara on Piazza di Santa Maria Novella last September. I highly recommend.