Lydeeya, have you looked at a map yet?
Maybe someone else will step in here and microguide you, the most I can tell you is that as you already may know, Trevi Fountain is not that far from the Pantheon and the Spanish Steps.
To me, the Pantheon is a must-see, as is the Colosseum. Get to the Colosseum early. Allow an entire day for the Vatican.
I love Piazza Navona as well as Piazza del Popolo. There is also the Campo d’Fiori.

Day 1 Christian — St. Peter’s , Vatican museums, Castelo St. Angelo, etc.
Day 2 Pagan — Palatine, Colosseum, Forum
Day 3 Plazas and people watching — Spanish steps, Trevi, any of the other Piazzas you didn’t cross in the first two days.

Visit the Pantheon either day 1 or 3 depending on your route.

Take the subway to the farthest thing you intend to visit each day and work your way back to your hotel/hostel. You may end up walking all the way or catching subway or bus if you get tired, it’s raining….

Although some may balk, with the limited time you have in Rome, I would recommend one day hiring a private guide. We did, and went to Trevi, Pantheon, and other sights. It was nice being spoon fed info, and we got to visit a lot of high spots. We would have never gotten so much info on our own, and with a private guide you tell them what you want to see. We did one in every city on our first day to get our bearings. A little expensive, but worth every penny.
That being said, the Basilica di San Clemente, the Colosseum, and the Forum are a nice jaunt for one independent day and in the same relative area. I would never not see San Clemente. Incredible. http://www.tripadvis…
Another rec is the Capuchin Crypts. http://www3.sympatic… Only 20 min of your time, but worth it.
And yes, get a guidebook and look at the layout. From doing that for our trip I know Rome better than my nearby Chicago and can still remember it 6 years later. You definitely need to know what you’re walking into. Happy travels!