Florence to CT with a stop in Pisa

If your main objective is to see the Leaning Tower and duomo, a few hours in Pisa could work. Trains from Florence are frequent.

It's just under 3.0hrs for the train ride to Riomaggiore from Florence. I believe that all train runs stop at Pisa but you will want to double check the large yellow paper schedule posted behind glass in the train station. At Florence, they are in a few places. Scan down the list for your departure time and look for the run that includes Pisa. Every stop of every run is shown.

Next, if you are on an R train (Regionale), which is most likely, your ticket is good for 6 hours after you validate it in the little yellow box at the train station. At Pisa, you can hop off, visit the tower and hop back on a train of similar class (another R train) for the remainder of your journey. From Pisa to Riomaggiore, you may have to change trains again at La Spezia Centrale. The reason you can do this hop off/hop on feature is that your ticket on an R train does not show a specific train or departure time. It's an open ticket good for 60 days until you validate it. You can't do this on the classes of trains that require seat reservations. No seat reservations permitted on the R trains.

Note that there is a staffed luggage storage facility at the Pisa train station. We have used it. With your back to the train station and facing the tracks, turn left (South) and go down to the last two buildings on your left. Go between these last two buildings and walk to the rear. You'll see it. Two years ago, it was 3Euro per bag. They used to copy your passport picture and keep the copy with your luggage. To get your luggage back, you have to show your passport. It was fine for us.

An afternoon in Pisa can certainly be part of the schedule. I'd also contact the hotel in riomaggiore and request a check-in for a later time. If you talk to them in advance there is a good chance that they may be able to accommodate you. And that would help you not feeling rushed.

We stayed in Lucca and daytripped to Pisa and the Cinque Terre. We left Lucca in the later morning (perhaps as late as noon once our train finally got there). By the time we got to Pisa, got a bus to take us to the tower, roamed around for a while, got a bus back to somewhere near the train station, found the train station, and finally got to Riomaggiore, it was around 3:30 PM. Keep in mind, we were originating in Lucca, not Florence; so add about an hour to that timeframe.
We did not climb the tower in Pisa for two reasons: the price and the wait. You can buy tickets ahead of time, according to RS Italy 2008; but if you buy them at the tower, it's apparently about a 2 hour wait, and 15 euro per person seemed a little steep (no pun intended!). Even though we asked the driver "quest' autobus va in stazione?" he dropped us off a few blocks from the train station, pointed in a general direction, and we had to take some time to find it. Hopefully you'll have better luck!
I got some beautiful pictures of the Tower, etc, and was glad I took the bit of time to do it.
buon viaggio!

We did just that. We left Florence and stopped in Pisa on our way to CT. It was very easy to do. We bought our train tickets at the American Exress office in Rome. I am sure they have one in Florence as well though the train stations are easy to manuveur. We ended up taking a taxi to the Leaning Tower area and had a nice lunch and walked the town a bit before heading back to the trains. Definitely doable. Enjoy.