Would 2.5 hours be enough to walk from Pisa Centrale train station, see the tower, grab a bite to eat and walk back to the train to Florence?
We saw the tower on a quick train layover. We took a public bus there and back. But will only have time to pick up a sandwich or snack at a bar; not enough time for a restaurant.
I think depending on how long you want to spend there, you could probably make it. It would basically be an "okay we saw it and cross it off the list" type of stop, esp if you want to grab food too. I'm guessing it will take about an hour walking there and back (returning several minutes before your train departs for Florence). An hour and half is enough time to see the tower and eat a quick bite (italians hate that phrase), in my opinion, but no dilly-dallying. Probably not enough time if you want to climb the tower and there's a line. We stopped in Pisa on our way from Florence to CT but we went by car. Absolutely amazing trip. Pisa was cool (been there before), but CT was PHENOMENAL (first time)! and Florence is always amazing. Enjoy your trip!
If you want to get into the Duomo, you have to stop and get a ticket there locally, not online. There can be a lot of people in line, of all nationalities (or just one bunch asking too many questions).
Rick suggests that it takes 30 minutes of direct walking each way, or twice that if you're looking at his walking tour route and trying to notice the details. Also, although the book says the bus departs across the street from the train station, in front of NH Cavalieri Hotel, we caught at the bigger bus stop on the station side of the street (so look both places).
If time is of the essence, then you should take a taxi because it's not a short walk, it's almost a couple of Km each way. The taxi will take you there in 5 min or so. If you just take the silly photo holding the tower, without going up or visiting the Duomo baptistery etc you can see it in 2 minutes then make your way back. 30 min total and you are back on a train to Florence. Check!
I don't think 2.5 hours is enough, assuming you have luggage with you. It takes time to check the luggage at the station. When I did it, albeit nearly 10 years ago, there was one attendant at the left luggage room. If there's someone ahead of you, you will wait in line. When I returned to collect my bag, I had to wait about 10 minutes because the attendant had gone off for a break. It's a short taxi ride so not expensive. Your choice: time vs money. In fact, if you don't have more time, it could be worth your while to hire a taxi for the entire time, dump your luggage in the trunk and have him wait for you and return you to the station. I don't know how easy it is to find a taxi outside the campus. By the way, there's more to see than just the tower (allow about an hour to climb it and buy timed tickets in advance). There's a beautiful church and baptistry too.
I found the walk between the train station and Field of Miracles interesting, so I wouldn't skip it. Take a cab to the Field of Miracles and walk back.
I suggest you buy 2 train tickets for the trip, one from Cinque Terre to Pisa and a second from Pisa to Florence. Almost all trains from Pisa to Florence are regional (R) or regional veloce (RV), and tickets for those trains are valid for any train on the date indicated on the ticket. When you're ready to leave Pisa, you simply validate your second ticket and board the next R or RV train. That will give you maximum flexibility should you finish in less than 2.5 hours or decide to stay a bit longer.