Florence accommodations

A quick search on this forum will yield lots of results, some of which are below:

https://community.ricksteves.com/travel-forum/italy/florence-hotel-db47a488-c306-49f4-adf7-2e0da55043d0

https://community.ricksteves.com/travel-forum/italy/florence-hotels-36fa3f30-33a1-422e-b5e3-2fa64c3e84ae

https://community.ricksteves.com/travel-forum/italy/hotels-in-florence-ca420497-09c0-4702-9205-715a5ab55b96

https://community.ricksteves.com/travel-forum/italy/looking-for-recommendations-for-hotels-in-florence

https://www.loggiatodeiservitihotel.it/en/index
In a quiet corner near the Accademia and just north of the Duomo.

Try any of the 3 districts of the Oltrarno (beyond the river Arno, on the south bank of the river):
San Frediano (south west of Ponte Vecchio), Santo Spirito (directly south of Ponte Vecchio) or San Niccolò (south east of Ponte Vecchio).
The Oltrarno is slightly less crowded with tourists, especially San Frediano and San Niccolò, although Santo Spirito is closer to the sights.

Unless you have a larger party which necessitates more than one bedroom, for 2 nights only, I would stay at a hotel rather than an apartment, since the check-in and checkout process for apartments is more time consuming. A hotel desk can also provide help and advice on a variety of things, while at an apartment you are on your own.

Last year we stayed in Firenze Number Nine. We loved this hotel. It's a quick walk to/from the train station. It's close to good restaurants. The hotel is also close to the cathedral. The concierge is wonderful and helped us with planning our trip's excursions.

I second NickB's recommendation for the Loggiato Dei Serviti. Nicely located, nice breakfast and nice rooms. I think my daughter and I stayed in the room Rick is pictured in at the end of his shows. My husband and brother-in-law stayed in a room that not only had a view but a balcony overlooking the Duomo. Every evening we would sip some wine, snack on some bread and cheese and a friendly cat would come by for crumbs and a little visit.

A third thumbs' up for Loggiato Dei Serviti. We stayed there during the Holidays in 2017 while visiting our daughter; it was a perfect location to be so near the Duomo and Baptistry, and to wander back to after spending hours at churches, museums and the Christmas Market at Piazza Santa Croce. The staff were friendly, the property is charming and many rooms offer nice views across rooftops, domes and courtyards. A great place to wake up and call it a day against Renaissance-101 backdrop.

I'm not going to recommend specific hotels, since I think you requested only neighborhoods suggestions.

Before recommending hotels, maybe we should know about your budget requirements. The Loggiato dei Serviti and Firenze Number 9 are in two totally different classes of accommodations. The Loggiato is a 3 star hotel where you can hope to stay for under $300 in high season and maybe half that in low season. The Firenze number 9 is a luxury 5 star hotel where you'll need at least $700-800 a night in high season.