Best neighborhood in Rome for two nights?

Our favorite area is Piazza Navona area (easy evening and morning walks to nearly everything)...Prati is too far out in my opinion. Consider a two bedroom AirBnB to give you a bit more space. Look for one with lots or reviews hosted by a "super host".

Centro Storico (Campo dei Fiori/Navona/Pantheon/Trevi fountain/Spagna) is the most central, and therefore the most convenient to be in the midst of everything (including the shopping), hence more crowded therefore more expensive.
Prati is nice in a residential area. Not as Central but the Metro runs near it.
Termini, not as central, but it is the transport hub well served by metro and buses. Also easier to get to the airport by train.
Trastevere is across the Tiber, but very quaint, It will make you feel like in a smaller medieval village. Well served by the no.8 tramway (light rail) to the Centro Storico, but they are replacing the tramway tracks now till the end of January therefore the no. 8:is now served by buses.
I usually stay in Trastevere, I like it the nest, but that is also because it is more convenient to visit family in Rome.

I’ll echo the recommendation for piazza navona/pantheon area. This is my favorite as well.

I have stayed south of the Vatican in an area west of the Tiber.. I’m not sure if it’s considered Trastevere but may be just north of it. Although this was further from city center it was still easy to navigate by foot.

I’m including a link to a previous post where I detailed my recommendations although you may be more in search of an apartment type accommodation so my recommendations may not fit your needs. If you do consider them just note that imperium suites does have an apartment style accommodation but if I remember correctly I read horrible reviews for that particular room type.

https://community.ricksteves.com/travel-forum/italy/venice-and-rome-hotel-recommendations

My favorite area of Rome is around the Pantheon, but it is more expensive there.

I stayed at this B&B. It's just off Via Del Corso. Perhaps you can book two rooms?
Walking distance to the major sites.
B&B Casa Angelini

Thank you!

We booked a room for 3 in October at CityLife Rome, which is a B&B. https://cityliferome.italia-it.info/en/
They are also on booking.com.
It's in the Termini neighborhood near the train station. We are only staying there for one night before heading home. For us this looked like a good option balancing nice accommodations (we want to end our trip on a high note, not at a budget hotel), location, and price. I'll be sure to report on the accommodations once we are home!

Our first trip in 2019, we stayed in a hotel on Via del Corso. We liked the hotel but the road was a little noisy at night. The AC wasn't very powerful so it was noise or sleeping too hot. However, it was very central. It was a 5 minute walk to Trevi Fountain one direction and 5 minutes to the Pantheon the other. It was also on the bus line to the Colosseum which was also walkable. I'd stay in the area again, just not on the main road.

In May, we stayed in a very quiet hotel in Trastevere. I really liked that area. Our hotel was set a bit back but there were a ton of restaurants. It had a good vibe. While we walked a lot, we ended up taking taxis to both the Vatican and Colosseum. There was public transportation but it was hot and this was at the end of our trip. For two days to do tourist activities, I'd stay somewhere more centralized. However, walking to restaurants was great.

I'm sure there are plenty of Airbnbs around everywhere.

We stayed in Monti in April and I loved it not touristy and 10 min walk to Colosseum we had 4 and stayed at Hotel Raffello our room had one king and 2 twin beds it was essentially 2 rooms great breakfast plenty of space I’d recommend it easy walk to train station