Cinque Terra - Day Trip or an overnight?

Absolutely overnight if you want to enjoy any of the charms of The Cinque Terre (note spelling). Pick a village based on an accommodation that appeals to you. Monterosso has the most lodging choices, but it is late for July reservations, so I would say any village but note that Corniglia is high above the sea and you need to take the little shuttle bus unless you like climbing stairs. It is a bit over 4 hours and takes 3 trains from Arezzo to Monterosso al Mare. Explore trains. at www.Trenitalia.com for whichever village you choose. Even Levanto is an option. It is only one town beyond the official five of the Cinque Terre.

USe Rick Steves' guide, www.Booking.com, or ArbaSpaa to search for lodging ASAP.

While your trip #1 is best for enjoying Cinque Terre, it leaves you with just one full day in Florence, which isn't enough time. Instead consider going to Cinque Terre on July 2, exploring the Cinque Terre villages that afternoon, doing an early morning hike the next day (when it's cooler and you can freshen-up before checking out of your hotel), storing your bags and exploring some more, and then taking an afternoon train to Florence on July 3. It's rushed, but it gives you the same 2 full days in Florence as your trip #2 option. Imo, 2 full days in Florence is the minimum you should consider.

A day trip to Cinque Terre is rushed and you will arrive, most likely, with all the other hordes of day trippers. If you spend the night, you can experience the mornings and evening, without all the tourists. Much more pleasant.