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.
All I ask is a tall ship and a star to steer her by; John Masefield
Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012, Dream 2013
Celebrity: Summit 2011
Princess: Ruby 2010, 2014, Caribbean 2013, Coral 2014, Regal 2014, 2016
Sail Windjammer: Mandalay 2017
Star Clippers: Royal Clipper 2015