Non-hotel accomodations in Florence and Rome

Have you considered monasteries?

https://www.monasterystays.com/

Are you going to cook and eat in your own kitchen of an AirBnb? That won't help you meet locals. And AirBnBs commonly harm the local housing infrastructure. You will find mostly AirBnBs around you in the major cities of the world. My suburban NJ town prohibits short-term rentals of any kind, as does my native Manhattan.

Will you consider a "real" AIrBnb, where the host lives there, and you get a single room? That would be a good way to meet locals.

Do you speak Italian? My Italian is very elementary, and I’ve found the easiest way to have conversations in Italy is staying in B&B’s where the owner also lives there, or they are frequently there. Taking any kind of class is another way - a cooking class, art class, etc. when the teacher, chef, etc. usually enjoy sharing and answering non-class questions, too.

You might want to also pick a smaller city that isn’t as touristy where you can find what you’re looking for in a wonderful local experience.

I tend to stay in smaller, family owned inns and BnBs. I feel that gives us more connection to people. Is that what you are looking for? I often find my lodging in the Rick Steves guide. Some feel Rick’s suggestions are not fancy enough, but I’m not a fancy person, and with the amount of travel we do, 5 star accommodations are not in the budget.

In Rome, we stayed at a small family owned hotel as a part of our RS tour. It was a great location with personable staff. Hotel Lancelot

In Florence, we stayed at a small place (no breakfast), wonderful owner who helped plan our Florence itinerary including obtaining museum tickets. Hotel II Bargellino

When I'm looking for accommodations, I go to Google Maps. Then I put in the neighborhood I'm wanting to stay at. Click on the Hotels block at the top of the page, and little icons pop up everywhere with the price noted.

Rome has all kinds of places to stay in. Many of them are B&B's with just a few rooms for rent. We usually stay in the St. Peters/Ottaviano neighborhood. The Vatican Museum and the Vatican are a close walk,

Last time in Florence, we stayed across the street from the train station until we rented a car and headed an hour south to an agriturismo (farm stay.) Agriturismos in Italy are where you get up close and personal with the people. Virtually ever farm in Tuscan has an apartment or rooms as an additional source of income.

Thanks for all the wonderful suggestions.