Barbee, my daughter and I stayed at the Domus Julia (apartment annex to the Hotel Julia recommended above), and we liked it a lot for the good value.

We did see this hotel you asked about, and it looked very nice. We walked into the lobby and picked up a business card at the desk:

La Lumiere di Piazza di Spagna (Spanish steps), has rooftop dining, is in an old mansion on Condotti street. More expensive than our Hotel Julia, I'm sure. www.lalumieredipiazzadispagna.com.__