Just to add to the list.
We stayed at the Hotel Artemide Roma - it is relatively close to Termini Station if the train plays into your plans. It was an easy walk to Trevi and a straight shot to the top of the Spanish Steps. Plus it was an easy downhill to the northern end of the forum, almost spilling out at the Alter of the Nation.
We booked directly with the hotel for about 240 Euros a night for a classic room that included free breakfast, wi-fi and mini-bar. The hotel has a beautiful terrace with distant views of the dome of St. Peter's.