I have seen day trips from Florence where they take you out to Cinque
Terre which would be great (has anybody done just a day trip there?) -
Also day trips where you can see a few surrounding towns/cities like
Pisa etc. It might sound crazy but has anyone done Venice in a day? 2
hr train from Florence ,and return?
I think we'll come back to what some of us cautioned earlier: you are not going to have the kind of time to do all this that you think you will. If you don't arrive in Florence until the afternoon of arrival day, you'll only have two full days there. As a fan of that city, I'll cheerfully disagree that two days are enough for that one if you want to do other locations from there as well.
The Amalfi, as stated, is quite some distance from Florence. The suggestion to substitute the Cinque Terre instead is a good one, IMHO, as it's MUCH closer to Florence and you'll get the sea views (plus hiking!!) without a large chunk of a day spent getting there. It also a much more enjoyable place to STAY rather than day trip as you'll get to enjoy the golden hours before all the OTHER day-trippers arrive and overrun the place, and after they leave. You could even make a stop through Pisa for an hour or so on the way, if you wish, although I probably would give it a skip.
Sooo, you might look at 4 nights/3.5 days in Florence with a day trip or two (Siena/Lucca) if ambitious, and 2 nights/1.5 days in the CT before heading off the Rome early the morning of the 7th. Personally, I'd save Venice for another trip as it deserves more than a day.