Florence neighborhood close to Duomo/historical center

We enjoyed being a short distance away from the crowds and chose to stay in the Santa Croce area. Make sure to visit the cathedral where many notables are entombed including Michelangelo.

Looking at the location filter options that Airbnb provides, Centro Storico would be most central but could come with noise. Quieter but still close areas would be San Marco-San Gallo and S.S. Annunziata, and Santa Croce can be fairly quiet too. Santa Maria Novella and San Lorenzo areas are very close but likely to be noisier. Two other generally quiet areas that are a slightly longer walk to the center are Sant'Ambrogio (just past Santa Croce) and Santo Spirito (across the river). The rest are a relatively long walk or bus ride from the center. I prefer quiet to maximum closeness and have stayed in apartments (mostly VRBO) in all 5 areas I've mentioned as being quieter.

Once you've identified a few good options, you can post again for comments on those specific locations. Be sure to include as specific a location as possible.

If you filter by neighborhood, anything within the Centro Storico is near everything.

AirBnB mentions the following:
CENTRO STORICO this is probably the entire historical center.
There are also additional neighborhoods listed, many are actually within the centro storico, therefore they are subsets of the historical center.
The ones that start with “saint” such as SAN, SANTO, SANTA, and SS (Santissima) are all neighborhoods inside the historical center.
The only exception is SAN JACOPINO, which is outside the historical center (therefore don’t select it).
The area of the Duomo is called SAN GIOVANNI, you don’t need to confine your search there as the others are close enough.
In terms of quietness that varies according to the specific street/Piazza. Therefore there could be quiet spots in busy neighborhoods like San Giovanni and very busy and noisy streets in quieter neighborhoods like San Frediano or Santa Croce. So it all depends on the specific location of the apartment. Tell us the address and I’ll tell you if the area is quiet or not.. Of course no guarantees. You could have an apartment in a very busy street which faces an internal courtyard and that apartment would still be very quiet.

We stayed at the wonderful boutique hotel on the Arno, a short walk to the Duomo.
It was the Hotel Balesteri.

From my walking around the city I would consider staying in the Oltrarno, literally the other side of the Arno, near one of the bridges close to the center (Vecchio, Santa Trinita, maybe Alla Caraira). Some of the sights are there and it's a more residential area, and a short walk the major sights across the river.

Florence is a very walkable city. So even if your hotel/airbnb is outside of the very center, it's not a long walk. I recently stayed right in the thick of things, and I did not find the noise to be bad. We were there in July.

Our 5-week apartment was on the far eastern edge of the centro, still within the old city walls. 15 minute walk to the Duomo. Very quiet and very few tourists. Nice neighborhood, Sant'Ambrogio, and the market is fun. Also not even two minutes from where the little electric buses stop.