St. Peter's/Vatican City
In order to come in you must be dressed properly (cover your shoulders and knees). Once in it's all abundance; the bronze canopy made by Bernini (the largest bronze monument in the world), Raphael's rooms (with the many frescoes), the Pieta by Michelangelo (sculpture of a young Mary holding her death son). And many other galleries with paintings, sculptures, tapestries and geographic maps. And there's of course the Sistine Chapel with walls and ceiling decorated by frescoes of Michelangelo. You also can walk underneath the dome or you can climb to the top for a fabulous view over Rome.
http://www.vatican.va/

Trastevere
Situated across the Tiber this is probably one of the nicest districts of Rome. Narrow street paved with cobble stones and with tables of the many restaurants. The center is the Piazza Santa Maria in Trastavere. Very lively at night and picturesque during the day.

Spanish Steps
In the 17th century this is where the Spanish ambassador had his office and the area around was considered Spanish. In those days it was at least as crowded as it is now. Day or night, you always find people hanging out on the steps. At the top op the stairs there's a church called Trinita dei Monti. At the foot of the stairs you'll find a fountain created by Bernini. It's a leaking old boat and the water is drinkable. The steps are most beautiful in spring when they are decorated with flowers.
Address: Piazza di Spagna
http://www.piazzadispagna.it/