Main points of interest in Palazzo Madame are Renaissance courtyard, Monumental Staircase, Maccari Hall, Italy Hall, Senators' Lounge (on the wall is a particularly fine sixteenth-century Medici tapestry with a large coat of arms and wide bordures, previously hanging in the Uffizi in Florence), Ostrich Hall (splendid sixteenth-century coffered ceiling), Risorgimento Hall (contains busts and portraits of some of the most important figures of the Italian Risorgimento), Signature Hall, Corridor of the Hero etc.
You can also visit public debates of Senate by prior appointment:
Servizio di Questura e del Cerimoniale
Visite ai Palazzi
Senato della Repubblica Piazza Madama, 11