In addition the actually staying in the Cinque Terre, I've also done a day trip from Florence. You might consider taking a slightly later train back to Florence so you can spend a bit more time there and enjoy a fine hot meal in one of the towns. I normally stay in Monterosso so I'm more familiar with the restaurants there, and Cantina di Miky is a big favourite with many here (in the "new town", close to the rail station). There's also the more upscale Miky (owned by the same family), especially if you like seafood.
If my memory is correct, there are some benches in the "old town" piazza, near the Duomo in Monterosso. There's a small park there. You could also "take a break" in any of the towns by stopping in one of the restaurants for lunch. Monterosso has two beaches, however some parts of those are "pay-per-use".
As a previous reply mentioned, you'll need a Park Pass for hiking any of the Sentiero Azzurro trails. I vaguely recall that the Monterosso-Vernazza trail is one-way at some times. All the information should be available on the Parco Nazionale website link that was posted in a previous reply.