Hi there, there are a couple of hop-on/hop-off bus operators in Rome covering nearly all the sights so you may want to take a look at them.
The main downsides are that they get very busy, and tourists aren't very good at queueing, so that & the fact that they run in quite a large loop means you should plan ahead & make sure you are back at the train/coach in plenty of time for the return journey to the ship.
We would normally look at their websites, download their maps & decide what we want to see, then work out the best way to get from each drop off point, i.e. can I walk past 3 or 4 sights & pick up the bus from that location instead of walking back to the point you were dropped at.
Once we know what we want to see, we try to make certain that we do the furthest sights first, so that we are getting closer & closer to the ship meeting point.
Hope that gives you some food for thought.
Alan & Katrina
Last Cruise: Minerva April 2015
Next: Royal Princess August 2015
Then: P&O Oriana October 2015
and : Queen Victoria January 2016
Golden, Grand(2), Caribbean, Sea(4+1 aborted)
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QM2(2), QE2(9), QV(6), QE, Caronia(2), Minerva, Minerva II, Fred.Olsen(8), NCL Jade, =X= Eclipse, HAL Ryndam, Aza.Journey