If you really want to experience living as an Italian in Trastevere (the best location to stay in Rome, in my opinion), I highly recommend Casa Rossi. Luana and Maurizio are wonderful hosts who go out of their way to make their guests feel welcome.
There is an elevator from the first landing to the fourth floor; the apartment is large and bright (if you need it to be dark, the shutters and curtains do that job well, too), and exceptionally clean. The linens are very nice, the beds comfortable, and touches such as fresh flowers, wine, coffee, water, yogurt, snacks and sweets much appreciated. The kitchen is fully functional and stocked with basics should you want to prepare a meal and the washing machine is such a welcome amenity, as is the remote wifi unit which was so useful when we were out and about. Wifi in the apartment is strong. As others have mentioned, the shower is a little small and takes some getting used to (it might not be the easiest for those with mobility issues), but the bathroom is large and there is a wonderful makeup mirror!
I just cannot say enough good things about Luana and Maurizio. They are lovely, warm, and helpful people who show their guests the very best of Roman hospitality.
Highest recommendation for Casa Rossi!