Vegetarian and Vegan is pretty easy in Roma. Real Italian cuisine is plant based
Stay at the Beehive, a veggie hotel/restaurant near Termini station. http://www.the-beehive.com/
For eats, try L'Insalata Ricca near Capo Fiori, Arancia Blu on San Lorenzo, and Margutta near the Spanish Steps (direction of Piazza del Poppolo on a side street to the right).
Be very, very careful that you are not pickpocketed on the metropolitana - they are world class thieves. I used to watch people get robbed every day and before you can react, they're gone.
If you are going to the Vatican museum, go early, don't take the audio guide (which you must backtrack to return), and once you are done in the Sistine Chapel, go out the back door which takes you right into St Peters.
Stroll down the via del Corso at the end of the day (as the Romans do)- its great fun.
Enjoy a late sunny afternoon on the Piazza Navona.
Go buy some fresh veggies at Campo Fiore - but get there early!
Set aside a full day for the Colosseo and Palatine Hill but start at Palatine and buy your day pass there (the line is much shorter). Then, when you go to the Colosseo, bypass the long lines by going to the left of them and going straight in (with your ticket). Decent eats nearby are avaialble at Cafe Studente (up the steps behind the Colosseo metro stop) or at The Sitar (Indian) across the street in the direction of Piazza Venezia.
I used to live in Rome and still live in Italy so send me a PM if you need more info. Non ce problemi!