In December 2023, we stayed here in Cannaregio for 10 nights and liked it very much --- you can see the mixed reviews and read mine: https://www.airbnb.com/rooms/31669467?source_impression_id=p3_1720609056_P32hmivBdxDPbypN
December 2014 (yes, SUCH a great time of year to visit Venice), we stayed here in Castello for a week: https://www.airbnb.com/rooms/1325679?source_impression_id=p3_1720609695_P3Ocrh17DHynj-P8
You can read my review although it's 10 years old. We loved the via Garibaldi neighborhood so much we went there again during the 2023 trip and ate lunch again at La Rampa. I did not read more recent reviews of this apartment.
As for "quieter," both apartments were quiet in winter, but I'm guessing that there is more noise at night in Venice in warmer months. I do not know if there are B&Bs or hotels in these neighborhoods --- we enjoy having a kitchen and kind of like having to monkey around with complex recycling systems, but a lot of people do not.
Anyway, we loved staying in both locations and it was super quick to walk or take a vaporetto to anywhere --- Venice is tiny.