Possible to do beach day trip from Florence?

It's possible! CT from Florence is about 2-2.5 hours by train, and in most cases you will connect through either Pisa or La Spezia. We did the same trip last year, but the reverse, starting in Venice and ending in Rome. Cinque Terre is one of our favorite places ever--so much so, that we decided to spend our first two nights there this year, as we are returning to Italy for a wedding. Beautiful, relaxing, great food (the pesto is to die for!). We spent two nights there between Florence and Rome, and I would highly recommend a stop/stay. Personally, I think 2-3 nights in Venice are plenty, so if you gave up a night there, and possibly one night in Florence, you could get in a two night stay. There are hotels in the "new town" Monterosso that are literally steps from the train station, with only a few steps to navigate. If you want to do the tour of all five towns, you can do so by train or boat, so the person in your party with knee issues will have an easier time. Have a great time!

Viareggio is a straitforward train trip from Firenze, and a interesting resort town with beaches, boats, parks, market area, and unique architecture. It's entirely level, and the 'boardwalk' is a quick taxi ride from the station.

You don't say whether you will be using public transportation or rental car, but I presume you will use public transportation.

The Cinque Terre is a favorite place among Rick Steves' herds. I am originally from Florence but used to vacation in Versilia (in the Forte dei Marmi or Marina di Massa area) during my youth, so the Cinque Terre was a frequent day trip destination from our beach house, since it was less than 1 hour away from Versilia.

The Cinque Terre is a beautiful area, but lately when I go there (generally to take friends and relatives from the U.S,) I don't enjoy the place as much anymore. I don't know if it's Rick Steves' fault, but the place has become a zoo crowded worse than Disney in Summer. Last time I went, just a few years ago, I took some American friends of mine the first week of May, on a weekday by car from Florence. It was only early May, yet the place was already crowded like a Summer weekend when I was growing up.

Also, by car from Florence it's a 2 hour trip, but by train it's at least 2.5-3 hours from Florence, because you will have to take three trains (2 changes, one in Pisa and one in Spezia). So if you crave a beach day while in Florence, and you are traveling by train, I suggest the following options that are much faster:
1. Viareggio
2. Quercianella
3. Castiglioncello
The first is a famous large beach resort town. It's the Florentines' no. 1 destination since it's the most easily reachable from Florence. It's a vibrant town with life resembling Miami Beach more than anything.
The no. 2 and 3 are smaller and much quieter. The beaches are smaller and rockier since the sit on a sort of a cliff. They are pretty, but much more laid back than Viareggio.
All of the above are the most easlly reached destinations from Florence if you don't have a car.