Just saw this ... if you've not yet gone, here are some thoughts ...
Florence - can find plenty of wine tasting and Tuscany excursions. Different durations and levels available. Perhaps they are touristy but can be quite fun if a day in the country might be your pleasure. Also, day trips via train to Sienna for the piazza and cathedral, to Lucca for bike ride on wall, or to Pisa for the Tower/Baptistry/Cathedral. Used to be an excellent gelateria on the path back to Pisa Centrale train station. A longer trip to San Gimignano? Interesting local wine (vernaccia) a few remaining towers, the BEST IN ITALY gelato shop in the piazza. Might a dinner up the Florentine hill be interesting? I think it is easy enough to get up to Fiesole. See the gardens, have a twilight dinner with a bit of sunset and views back into the valley. Finally, a tourist can hire a city guide for a period to time (half-day or a day?) to see stuff that just doesn't get noticed by everyone.
Consider less touristy things to do.
The Central market (indoor and outdoor) is a fun walk through. Take precautions with personal items as pickpocket is a skill honed in such places where less vigilant walkers are a mark. Find a small grocery store (un negozio alimentari), buy your choice of sliced meats & cheeses, etc., plus a panino (think baguette or ciabatta roll), something to drink, and voila' (sorry, that's French! Italians would say "ecco la!" = "here it is"). You've got a lunch for a place like Boboli Gardens park bench (next to Palazzo Pitti across the Arno River Bridge from the main tourist attractions). Nature and people watching - it's very Italian. BTW, there is an excellent outlet for fine leather gloves on the path to Boboli close after you cross the bridge - Madova, they have a web site. Not inexpensive, buy my gloves from there purchased in late 1990's are still in very fine condition! And, gloves don't take up much of what little luggage space you likely have for your trip. Consider stopping at Caffe Gilli in the Piazza della Repubblica for a brioche and caffe (espresso, please. Cappuccino after 13:00 isn't Italian! Watch the street life. There are great little gift boxes of sweets should you need something for friends not sharing your excursion. If coffee doesn't work for you, consider an aperitif alcoholic beverage: "uno spritz con Aperol" ... Prosecco + Aperol (orange) + soda water, or a Campari-soda, or a Negroni ... 3 very common lighter drinks that work well for people-watching with not too much buzz. Or, just order up a "Coke Lite" and experience a Diet Coke with a little different taste from what we drink here in USA. Viva la difference! (Oops, more of that French!)
I gotta say that in my 4 trips to Firenze, I found just walking to be a really fun way to spend time. Do some homework on line or in a bookstore/library (it's fun!) Consider if hiring a guide is a budget fit, and remember the hotel concierges might offer some good ideas ... and a map.