The dome to the left of Saint Peter's is the dome of the circular Borromini Church of Saint Agnes in Agony, the center of the Palace which serves as the northern backdrop to the Bernini fountain of Piazza Navonna (which piazza begins right across the street from the university).
Just to the left of the Saint Agnes dome you see a monument in the trees: that is the Garibaldi monument up on top of the Gianiculum Hill. My house (at Piazza Farnese) is equidistant between the two piazze (Navonna and Garibaldi), veering just a little south of the straight line (a twenty minute walk to the Vatican). I live in what is called the Centro Roma (Rome Center) neighborhood, the oldest part of the city.