Didn't realize that you hadn't booked your CT accommodations yet. It's rather late in game for high season so you are bound to have some difficulties there. I'm sure our choice filled long ago (La Spiaggia in Monterosso) but if you can't find anything left which suits your taste and budget, give a look at staying in Levanto? It's technically outside of the CT - the next town north of Monterosso - but trains are just as inexpensive from there as between the CT's five villages, and is included on the combo train/trail pass, should you purchase one. We haven't stayed there but I've read good things from other travelers who have.
You will need a pass to hike the CT trails, and those are available either with or without transport services. If you only take a train 2 or three times a day, it's more economical to buy individual train tickets but some people like the convenience of the pass combo. Just remember to validate it before climbing on that first train. As at least one, if not more, of the more popular footpaths between villages will be closed for repair, you'll most likely be making some use of the trains. All five villages are well worth a wander, and doing so will take the better part of your time there if you climb to their upper reaches, stop into the churches, explore tiny back passageways, etc.
As far as what to see in Florence and Rome, that's entirely up to your interests and time but my own votes:
Rome: most have the Vatican Museums on the list but from a hindsight perspective, Galleria Borghese was our personal favorite of the two. It has EXCELLENT crowd control, a superb collection, and the villa which houses it is just fascinating. Reservations in advance are mandatory, and you choose a specific 2-hour time slot. If you're interested, I can provide the link for doing that online. It 's closed on Mondays.
Other of my must-sees are the Pantheon (free), the Basilica of Santa Maria Maggiore, Archbasilica of San Giovanni in Laterano (free), Santa Maria del Popolo (free), the Colosseum, Forum and Palatine (do all three on one day: ticket covers them all), and a cruise of some of the piazzas: Navona, Del Popolo, Campidoglio, etc. These can also be done in the evening to save sightseeing time. You could also elect to see just St Peter's Basilica, if you decide to skip the Vatican Museums: free but can have a long security queue.
Florence: Uffizi and Accademia: do order tickets in advance to skip the line (I can provide the link). Go up to Piazzale Michelangelo for a terrific view of the city, and climb up a bit farther from there to San Mineato al Monte (free). You'll want to see the Duomo (free, and which we found more impressive outside than in), and the Baptistry is well worth the ticket price. Michelangelo is buried in lovely Santa Croce (small entry fee), and you'll want to get a good look at Ponte Vecchio, although it's best seen anywhere but on the bridge itself. Take a stroll through Piazza della Signoria - I like that one at night - and I'm a big fan of Convent San Marco and the Bargello as well.
Be warned: the Uffizi is wonderful but vast so it can easily eat up a good chunk of a day if you enjoy art. The Accademia is much smaller so won't take nearly as long to do.
