Just got back from two weeks in Italy last week, Milan/Venice/Florence/Rome. Echo the comments about renting an apartment or house. I'm 72 and was traveling solo, so I rented a small one BR apartment in Florence through VRBO and it worked out well. You should be able to find something between the SMN train station, the Duomo and the Arno River where I stayed that would accommodate all of you. Much less than for rooms in a hotel and from that area you can walk almost everywhere in the city center, except maybe the Piazzale Michelangelo which is high on a hill across the river and the best view of the city and Duomo. Take bus #12 from the train station and walk down to and across the river if you're fit. Otherwise bus #13 returns you to the train station, or any stop along the where you'd like to get off.
What is your price range for lodging? A few years ago in September we rented a two BR apartment in Florence through a real estate company named Pitcher and Flaccomio and were very happy with them. Go to their web site http://www.pitcherflaccomio.com/ and click on Rentals, the part of the city you want, how many bedrooms and see if they have something you like. Mid-September can still be a bit crowded and they may require a minimum week long stay, but it never hurts to ask. When you see the prices they may sound high until you add up the cost of three hotel rooms for four nights plus eating out every day. You should also consider that you can shop the markets for fruits, veggies, meats and even flowers and cook in the apartment, which we did.
One recommendation. Look up Trattoria Sabatino which is a family owned restaurant across the river, about a 20 minute walk west of the Ponte Vecchio. A friend told me about it and the food and service were to die for. They don't open until 7:15 PM and it is a beautiful walk along the river. Google the restaurant and you can see their web site and route. Also, if you don't know Italian download Google Translate, which will let your smart phone hover over Italian writing and turn it into English as you read it. Great for menu's, shopping, and even placards in Italian in museums. Have a great trip. I just did.
Jim