Hi, Niki,
Florence is magical. You could spend three nights or three years...you will fall in love. If the museums are closed on Monday, see the churches. Visit the Duomo, climb to the top of the dome for an amazing view of all Florence. 463 steps! Now you can have gelato! Visit the Baptistery and the beautiful mosaics inside. Look at the famous (reproduction) doors and make a note that you'll see the real thing at the Museo dell’Opera del Duomo di Santa Maria del Fiore. https://duomo.firenze.it/en The Duomo complex seems to be open on Mondays. Double check that! Just walk through Florence and get acclimated. Rick's walking tours are great. https://www.ricksteves.com/europe/italy/florence-itinerary
The Bargello seems to be open on Monday! https://bargellomusei.it/en/museum/museo-nazionale-del-bargello/ It has the most important collection of Italian Renaissance sculpture in the world.
The Uffizi Gallery is always busy. https://www.uffizi.it/en/the-uffizi You can get a timed reservation to enter. https://www.uffizi.it/en/pages/how-to-book-tickets You also might consider an evening visit on Tuesday--they are open until 10:00 p.m. on Tuesdays. The Uffizi is enormous, and you could spend hours there.
If you are a Michelangelo fan, don't miss the Accademia Gallery. https://www.galleriaaccademiafirenze.it/en/ Also closed Monday.
My suggestion for all the museums is that it's worth going first thing in the morning or finding a timed-reservation entry. If you know you want to see the Uffizi, Pitti Palace, and the Boboli Gardens, there is a 5-consecutive day ticket called the "PassePartout 5 Days" that will save you a few euros.
While you are visiting the Pitti Palace and the Boboli Gardens on the other side of the Arno, have dinner in Oltrarno. Be sure to go to Piazzale Michelangelo for the postcard-perfect view of Florence https://www.timeout.com/florence/things-to-do/florence-oltrarno-guide
The tombs and monuments in Santa Croce are another highlight of Florence. https://www.santacroceopera.it/en/
This is a useful site for the sights: https://www.visitflorence.com/
Your hotel is a 10-minute walk from the Duomo and a 13-minute walk from the Uffizi, which seems convenient to me (I don't know the hotel at all). It seems to have great reviews and responsive staff (TripAdvisor). If you wanted a bit closer, we loved B&B Soggiorno Battistero. https://fortehospitality.it/en/soggiorno-battistero-en/
Eat all the gelato! https://www.visitflorence.com/eating-and-drinking-in-florence/gelato-in-florence.html
Siena is lovely. We took a bus from Florence to Siena and spent two nights there. Hotel Alma Domus. Room #5 has a great view. https://hotelalmadomus.it/inglese/index.php You could easily day trip to San Gimignano from Siena if you were interested in another night elsewhere.
I clearly have opinions...hope some of them are useful to you! Have a wonderful time! (just saw your recent posted itinerary--you will DEFINITELY have a great time!)
One more thing--I saw you were interested in a Vatican tour while in Rome. We LOVED this one at night--it felt like we were there as VIPs. https://www.thevaticantickets.com/vatican-night-tours/