definitely possible to do a day trip from Florence
Ciao Anna and welcome to our forum!
Yes, once you're in
Cinque Terre the easiest way to move around between the towns is by train (or by foot through the trails - the most southern of the five towns are really close to each other and the trail is pretty flat between Cornaglia, Manarola and Riomaggiore). It is also easiest to go by train from Florence since you then don't have to worry about your car and driving the steep roads there. It is a national park and space is limited so driving is not encouraged.
We went in April taking the train from Florence, it was about a 2 1/2 hour trip. We took the 7.50 am train from
Florence to
Monterosso, changing trains in
La Spezia and got in at 10.17. We had decided to hike all the way down the Cinque Terre and started at Monterosso because the most difficult part of the trail lies between Monterosso and Vernazza - lots of steps to climb up around a mountain and then to descend into Vernazza. We had decided to spend the night there so that we wouldn't be in a hurry to get back to Florence so you can do that as well, maybe toward the end of your week in Florence.
You can also do it all in a day - you don't have to hike the whole trail (takes 5-6 hours) - since the train connects each of the towns so you can hop on and off and just visit the towns without doing the trails or maybe just a part of the trail. The most famous part (and easiest as it is short and flat) is the "
Via dell'Amore" (Way of Love) which is the part that joins Manarola to Riomaggiore (the last two towns south). Just make sure to get a park pass that includes train travel so that you can use it unlimited times.
You can read more details about the Cinque Terre on our blog post about our
weekend at the Cinque Terre.