We will visit Rome for the 4th time in March 2027. In the past we've stayed there for various lengths of time (3,4, & 7 days) but this trip will be between at least 14 days. What we've just loved is the rhythm of the city, specifically the Campo de' Fiori piazza area. Some would call it very touristy, but in the offseason each time I've become addicted to daily vibe of the vendors setting up shop for the market at 6AM, doing their business, packing up and being out of there by 3PM. After that, the piazza is an evening gathering place for young people that convene by the Giordano Bruno statue. It can get a little noisy late at night, but I consider that wonderful white noise to sleep by. During the day--virtually anything I want--bakeries, restaurants, movies, farmacia, lavanderia, caffe shops...literally steps away.
It is a somewhat pricey area, but very safe and for a one bedroom, one bath AirBnB, you should be able to secure one in the $200/night range. Hotels will definitely cost more than that. Easy walk to Trastevere, or the other way Prati. Probably a bus ride from the Vatican, although walking it's probably not much more than a mile or so.
Enjoy your planning!