Bella Roma!

*Sigh* Rome....
Beautiful city with lots of history. One thing is true you can never see Rome in one day. But!! I have a plan for you! I have been to Rome many times for Education, work and holiday purposes! I found a way to see all the important monuments and spots in 8 hours!!

Things you must see in Rome:
Piazza San Giovanni
Colosseum
Arco di Costantino
Foro Romano
Campidoglio
Teatro Marcello
Quirinale
Piazza Venezia
Fontana di Trevi
Trinita di Monti
Piazza del popolo
Castel San Angelo
Citta del Vaticano

They're listed in order from where you start. Start at Piazza San Giovanni and walk your way up towards Fontana di Trevi to Piazza del Popolo and then walk west towards Vatican City.
Of course if you have more days and time you should definitely explore more. But this is a quick list of places you must see!

Will jot back with more details.