1-Town to visit on trip from Rome to Florence? 2-Suggestions for Florence day trip itinerary?

Thats a tough one. I would say stop in Orvieto on the way to Florence but I do not remember seeing a place where you could leave your luggage.
This site says there is
https://www.tripadvisor.com/ShowTopic-g194843-i1755-k7716291-Store_luggage_at_train_station-Orvieto_Province_of_Terni_Umbria.html

You can see Siena and San Gimignano Chianti on the same day
But only by doing something escorted like this because the public trans is limited
https://www.getyourguide.com/florence-l32/san-gimignano-siena-and-chianti-full-day-tour-t7679/

Be aware that you can't hop off the train in a town between Roma and Firenze and then hop on another one, you will need two tickets: Roma to ??? And ??? To Firenze. You only have a specific amount of time to complete your travel on city-to-city tickets. And if you are taking a fast train, you will have a reserved seat on a particular train number.

You can see Orvieto as a daytrip from Roma (a little over an hour each way).

The other cities you mention are easy by bus or train; I agree with Jazz that perhaps an organized tour would be a good choice for your group to visit several cities in one day, and still have enough time for Firenze. Another idea would be to let the group split up for a daytrip if some people are more interested in a place and others are not.

The OP does not state where she is coming from. I would not try heavy touring after a long flight, if this is the case; better to go directly to final destination, get an accommodation, and maybe walk around the accommodation but ready to go back if too tired.
(But maybe we should not assume the OP will be jet lagged.)

As for Rome to Florence trains, they work this way: there are two parallel railway lines, the old slow line and the fast line, that has no stations: all the stations are on the slow line. There are frequent interconnections, so for example a train can travel on the fast line and call at Orvieto by switching for a few kilometers to the slow line. But in railway practice, high speed trains (AV = alta velocità) travel on the fast line and do not stop. These are the trains doing Rome to Florence in 90 minutes (a travel time you cannot match driving as the fast line is authorized for speed up to 150 mph). Regional trains use mostly the slow line, intercity trains a mix of both. This means that if you break the trip you have to use slower trains that will make the total travel time much longer.

There are several stops along the slow line, but the only places of tourist interest are Orvieto, Cortona-Camucia (a small station where intercity trains do not call) and Arezzo. Orte, Chiusi and Terontola offer connections to other lines but have limited tourist interest.

Thank you so much for the quick responses! This is great info and advice.

Jazz+Travels, I looked into that tour and I think we will book the one you suggested! Thank you so much for linking it. It looks amazing. The cost is very reasonable, and seems to be the same price or cheaper than a train to each of the cities on the itinerary. In one day this tour covers 3 of the places we want to visit! Very exciting! Thank you!

Zoe, I like the idea of splitting up if we need to. 6 people traveling together can get tricky trying to make sure everyone gets to see what they want to see.

lachera, we are coming from the U.S. Our flight is an all-night flight and we arrive in Rome in the morning. We're planning on staying up all day and not taking any naps because we will need to be able to sleep all night that night. I'm sure we will be jet-lagged, but also very excited and ready to see some tights. But I think you're right, maybe just strolling around Florence after we check into our flat will be a better idea. Also- very good to know about the slow line vs. fast line. I think after our long travels, the fast lane to Florence will probably be best.

Thank you again for the advice!

Where in the U.S. ?? Makes a big difference in your jetlag if you're zipping into Rome direct from JFK or spending 12-14 hours from the West Coast or making domestic connections. Just want you to be prepared.

We're flying from Atlanta to Charlotte, then Charlotte to Rome. I think it's a 12 hour trip.