If you're looking to stay for a few weeks, or a few months, I highly recommend Eugenia and Massimo's place in Monteverde. They were fantastic hosts, and the apartment is beautifully kept with all amenities. Massimo's office is nearby the apartment, so I felt very safe and secure at all times. They catered to many requests for me (e.g. Call forwarding, or additional cleaning, or mail delivery, or drycleaning), that I felt I had nice parents looking after me. They made my stay in Rome fantastic and convenient, and the apartment has every detail taken care of. They have a nice folder in the apartment with clear instructions for everything, and are available to resolve any issue immediately (e.g. I had a small problem with the washing machine, and Massimo had it fixed immediately). Being new to Rome, I was feeling a bit overwhelmed and intimidated, but knowing that I could reach Eugenia or Max, I felt very secure and comfortable. They also looked after my family when they were visiting and I was at work, and they have a very nice cleaning lady who can come on the weekends, whenever you request. The apartment itself is in a very nice area on top of the hill, few mins from Gianicolo park, although there's a slight downside that it is not easily accessible by Tram or Train - its usually a 20 min walk to get there, unless you can find the bus that rarely ever comes. However, there is a Taxi station that is nearby and sends taxis almost immediately. If you want a peaceful Roman experience with access to sights, but also some local experience, then I highly recommend staying here.