We've done it once when we couldn't get any reservation in any of the 5 CT towns. You can chalk that up to first timers in the CT. We stayed at the Astoria which is about 5 blocks from the train station. We booked it through www.venere.com. We were in their newly renovated section. Very nice. There is also the Continental which is about 500 feet from the train station.
Even though August is the height of the travel season, you shouldn't have trouble getting on a train for the routes you describe. There are about 45 trains a day from Rome to Naples. These are primarily Eurostars. Same from Florence to La Spezia.
I just haven't this quantity of trains sold out. However, as a backup, there is a couple of hints. 1) Buy first class. 2) When all trains seem to be full buy tickets on the local Regionale train to where you are going. I believe I described the R train to you in another message. No seat reservations permitted. Buy your tickets and show up early. As soon as passengers get off, you get on a grab your seats. It's like your local bus system. On the Regionale, if the seats are full, you can stand.
If you want your tickets in advance, you can purchase them at additional expense from www.raileurope.com. But remember, from Florence to the CT, you will primarily be on R trains. So RE can sell you a ticket but the same rules apply as above. No seat reservations permitted. Again, you will have to show up early and go for it.
