I'd appreciate opinions on what you found more enjoyable and convenient.
I'll be flying into Florence for the day and heading to Rome that night or early next morning.
My automatic answer would be stay in Florence because you are already there, but it depends on your interests and where you've been before. Also the season: when in the year will this be? The Cinque Terre (which will already be an extremely long "day" trip and may not be logistically possible) are essentially closed in the winter off-season.
If you only have the one day I would suggest staying in Florence and seeing some of it.
Florence is my choice of your options, for a day or a week. Lots to see and explore. Easy train to Rome.
Why fly to Florence if you need to go to Rome so quickly? Flights are usually cheaper to Rome.
Agree with the PPs. Cinque Terre is much too far to attempt with only a partial day. And to me it makes no sense to fly into Florence and not spend your time where, given all it has to offer.
I'm also agreeing with the previous posters. Cinque Terre is too far for a day trip. IMO, Pisa is not worthy of a day trip at the expense of Florence. If you have "seen" Florence, there are better choices for a day trip.
Why are you flying to Florence if you don't want to stay there? There may be a better choice.
Sounds like you like everyone else has been to Florence (it's such a a cliche) before so go with both Pisa and Cinque Terre. But did you research first how long it takes to get there from the airport before considering.
FLORENCE,
It seems the majority agree on Florence.
Thank you all for your response!