Rome
Excited to see "the old stuff"
The oval shaped Coliseum was constructed during the reign of Emperor Vespasiano, and completed in 80 AD. It took 10 years to build and, at the time of its completion, it was the largest structure of its kind in the ancient world. The name Coliseum is thought to have come about because the structure was situated on a site next to Nero's huge statue of Colossus.
The Coliseum was built solely for the purpose of providing a venue for various forms of public entertainment. For centuries, it hosted such events as gladiator fights, mock naval battles and exotic animal combats.
The famous Spanish Steps ("Scalla di Spagna", or "Scalinata della Trinita dei Monti") were designed by Francesco de Sanctis (1723-1726) after generations of controversy. When the Victorian novelist Charles Dickens visited Rome, he reported that the Spanish Steps were the meeting place for artists' models, who would dress in colorful traditional costumes, hoping to catch the attention of a wealthy artist. The steps are now a popular place to sit, write postcards, take photos, flirt, perform or just watch the passers-by.
The Pantheon was rebuilt in A.D. 117-125 by Emperor Hadrian to replace an earlier temple designed by Agrippa in 27 B.C. The original rectangular temple, consisting of sixteen single granite columns, became the porch for the newly devised dome structure. Once the Romans learned to use concrete, they were able to mold on the ground their rounded tops for their buildings and hoist them into place on top of a rotunda. The Pantheon is just such a structure with an opening at the center top of the dome. Because this opening is not covered, the floor is slightly concave with a drain at the center so as to catch the rain when necessary. 

The inscription translates as follows (thanks to Brent for the translation!) M.AGRIPPA.L.F.COS.TERTIUM.FECIT, translates literally as "Marcus Agrippa Luci, three time consul, built [it]".  In essence, however, this is just Agrippa saying "I did this!".
Trevi Fountain. A legend says that it is lucky to throw coins with one's right hand over one's right shoulder into the Trevi Fountain. Throwing one coin in will ensure that the thrower will return to Rome. Throwing two coins ensures that the thrower will fall in love with a beautiful Roman girl (or handsome boy), and throwing three coins in ensures that the thrower will marry that girl or boy in Rome. The fountain at the juncture of three roads (tre vie) marks the terminal point of the Aqua Vergine one of the ancient aqueducts that supplied water to Rome.
The Monument honors Victor Emmanuel, the first king of Italy after it was unified. It serves a dual function in that it is the home to Italy's Tomb of the Unknown Soldier, and military guards stand watch over its eternal flame.  And its lots of fun to climb all the steps- just don't try sitting down.  This is disrespectful, and you will draw the attention of the guards
From inside the Vatican
The Basilica Di San Pietro (St Peters) in Vatican City rests on the reputed site of St. Peter's tomb.