The Vatican
You haven't been to Rome, when you haven't been in the Vatican, this small catholic state in the heart of the city. Of course there is this big square, the St. Peters square, visited by tons of people every year and every day of the year. Go inside to the Basilica of St. Peter, and admire the Sistine Chapel, famous for Michelangelo's paintings on the ceiling. Avoid the long queues and buy your tickets in advance....