A:  In Trastevere, near Piazza di San Cosimato! This lovely, historic neighborhood is home to spectacular piazzas, majestic churches, and countless restaurants. Its charming, narrow streets are truly irresistible, and are the heart of Roman summer evenings.

Here's more:

• Apartments will house 2 - 6 students (depending, of course, on the number of bedrooms). You can expect to share a room with one other person, and  roommate preferences can be accommodated in most cases. Twin beds are the norm.
• All apartments are fully furnished (including a washing machine), and have wifi. Bed linens and towels are also provided.
• Our apartments are interspersed with those of "real" Italians, so you will have a truly authentic living experience!  
• Most apartments are located about 20 minutes (walking) from the American University of Rome, where classes are held. 

 
See pictures of the apartments at Your Place in Rome.