Be careful where you book tickets from, there are so many third party online websites which make themselves sound like the only way to get the best tickets. They just seem to sell at a markup to me. We got hit with Vatican Museum early entry tickets that way - we paid FAR too much wtih a third party seller and you end up hanging aroudn waiting for everyone to arrive. And still have to queue. Use the official sites direct with the venue - always ending in "it". Book in advance (at least a month ahead during summer).
Look at where the main sites are on a map and plan so that you see all the things in one area at one time so you're not going backwards and forwards unnecessarily.
We;ve been twice now:
First time was a city break (we arrived just after lunch and then had the next 2 full days in Rome and then took an early evening flight the day after that) and we stayed at a hotel right at the Pantheon on the square - it was amazing. We opened our window and could almost touch the pantheon, there was an opera singer in the square outside, a buzzy atmosphere. We walked everywhere as I feel it's the best way to get the proper feel of a city and it's a fantastic city to walk around. The furthest place was to the Vatican museum. Piazza Navona, the Campo Fiori market, Trevi fountain and Spanish steps were all close by.
We had combined tickets to the Colosseum and Roman Forum (again, third party seller, so expensive). We did that in the afternoon of the day we got there.
Went to Vatican city area early morning next day and went in the Vatican Museum (the busiest place I've ever been in my life akin to the London Underground at morning rush hour, it was literally shuffling along, it was so claustrophobic I didn't enjoy the Sistine chapel when we got to that bit and just wanted to get out). You can go in St Peter's Basilica for free as it just operates as a normal church too, but unfortunately it wasn't open on the day we were there till later on and we didn't have time to hang around.
We had a coffee in Piazza del Popolo then went for a walk around the Villa Borghese gardens.
One evening we went to the Travestere area for dinner - that was buzzing and atmospheric.
I love love LOVED Rome! We just came back off a cruise last weekend and had a day in Rome from Civitavecchia. We chose to see the stuff we hadn't already seen - St Peter's Basilica, had lunch in Trastevere, then went to the Castel Sant Angelo, then back to the ship. I think the others on our cruise felt there was too much to try and see and they felt rushed. It was their first and only visit to Rome. It definitely is a city that takes a return visit if you only have a weekend.
You will love it all and I'm so jealous. Enjoy just strolling through those little back streets finding a nice little local restaurant.....