Before you go to Rome, buy the Oxford Archaeological Guide to Rome.
Review the website listed below which is about underground Rome. http://www.romasotterranea.it/homepage.html
See the Museum of Roman Civilization which has among other things a recreation of the 2nd century Rome from the Forma Urba..
Count how many words in this post are standard English and yet are also perfectly good Latin.
When you see a giant marble head, or hand or foot, recall that Romans often made their cult statues (the image of the God for the temple) in a way that economized on the marble or other stone required. The head, hand, and feet are what was exposed of the statue, the rest might be in a toga and therefore did not have to be carved (not to mention quarried, transported, etc).
When in Rome keep your eyes open for the family name Colonna. I am friends with Kerry Colonna who worked with us at deGraf/Wahrman. The Colonna mansion and private art collection, one of the three most prestigious private art collections in the world, is open for tourists on Saturday morning each week. Go see it.
See the great sewer of Rome, the Cloaca Maxima, built in the time of the Kings. A good article on the history of the Cloaca Maxima can be found here.
Read about the time I first saw a Roman ruin in this post.