Day trip options from Florence - recos needed

4 Nights in Florence is really just 3 full days plus a few hours the day you arrive, so if you take 2 days trips, all you have left for Florence is only a day and maybe a half day on the day of arrival, depending on when you arrive.

Having said that, the best (fastest as well as cheapest) way to get to the Cinque Terre is by train. It's not a short trip since it involves at least 2 trains if not 3.
You can see your options by going to the train company website:
www.trenitalia.com
Enter from: FIRENZE TUTTE LE STAZIONI (Florence all Stations) (Note A).
To: NAME OF VILLAGE (Note B)

(A) For departure station you should select all Stations in Florence, rather than only Santa Maria Novella (the main station), because there are fast trains that go there and which call only at the FIRENZE CAMPO DI MARTE station (Florence 2nd largest). The train departing from there is a FrecciaBianca, a high speed train, which departs early in the morning, but gets you to your destination faster (you will need to change to a regional train at La Spezia, the city just before the Cinque Terre.

(B) As the name implies (Cinque means 5 in Italian), there are five villages you can choose, from East to West: Riomaggiore, Manarola, Corniglia, Vernazza, Monterosso. All of the 5 have a train station. The largest village (and the one with most trains, including faster Intercity) is Monterosso, which is the furthest to the west. The most visited is Vernazza (the village before Monterosso).

I have no tour companies to suggest for the Chianti area.

Hey splatt405, we traveled to Italy last fall for the very first time and totally loved our experience. We signed up for a day trip to Sienna Tuscany while we were n Florence. Our daughter and sil signed up for a day trip to Cinque Terre from Florence with the “Get Your Guide” app. It is an entire day trip, early start and finishes late but that’s one way to do it. Good luck!

ToursbyRoberto.com probably has something that suits your needs for Chianti, etc
He books up early

Great suggestions, thank you so much for the details!

@roberto, we get into Rome at 7am, so hoping for two full days in Florence. That said, do you think trying to do cinque Terre in a day is unrealistic? I
don’t want to be so exhausted I don’t enjoy our time!

You can do it in a day, if that is all you have.
leave early.

....we get into Rome at 7am, so hoping for two full days in Florence.

You won't have two full days if you are taking one of the 4 nights/3.5 days for the CT and one for Chianti. You'll have a partial, jet-lagged arrival day (if you are arriving in Rome from the US and traveling immediately to Florence) plus one full day. Even though you're getting into Rome early, don't underestimate the time it'll take to get through immigration, get out of the airport, travel to Florence, and find your hotel. You'll also need to drop your bags either at the hotel, if too early to check in, or at a bag-storage business if your hotel won't keep them until check-in.

Walk About Florence might be a good option for you. We did the Tuscany day tour and enjoyed it a lot. They also have a day trip to Cinque Terre.

We did the day trip from walk about Florence in 2015 and loved it, would definitely recommend it if you are interested in a full day thats planned out start to finish (lunch cost extra but was excellent).

The CT for about 4.5 hours on site, getting back in time for dinner, plan on spending about 7.5 hours on trains and going to and from stations

Thank you for the additional feedback! I’ll check out walk about Florence!

We just booked an all day Winery/Lunch tour from Florence with Prestige Rent which was actually Sold out for the entire month we would be there with one day open, which just happened to be when we could go, so I snagged it. I had never heard of this company but they had an Award from Trip Advisor and great reviews.
If you do an internet search for Cinque Terre tours from Florence you will find a few great companies, I would go to tripadvisor, read reviews, look at pictures then see which ones have availability for your dates.