Buongiorno,
Three weeks in Tuscany gives you ample time to explore in a leisurely manner, enjoying the museums, monuments and sites. Dividing your time in two, possibly even three, locations sounds like an excellent idea. You may even want to play with the idea of different types of accommodations during your stay (a hotel in the city, a B&B in Chianti and an apartment closer to Val d’Orcia). Of course there are so many to choose from your head will spin!
Spending time in the city will allow you to visit so many of the wonderful sites without rushing it and risking the famous “Stendhal Syndrome” ;-) My favorite museums, besides the classics like the Uffizi, Accademia, include the Cathedral Complex, Bargello and Bardini.
A B&B would be my first choice, some suggestions are:
Antiche Dimore Fiorentine
http://www.visitflorence.com/historical-florentine-homes.html
Casa dei Tintori
http://www.visitflorence.com/floren...ral-bed-and-breakfast-de-charme-florence.html
Villa Antea
http://www.visitflorence.com/florence-bed-and-breakfasts/villa-antea.html
As a second stop, head out towards Chianti, and spend your time exploring the vineyards, small towns and ancient churches. I particularly suggest that you look outside Chianti Classico, maybe towards western edge of Chianti.
Casolare Libbiano - with its onsite restaurant
https://www.discovertuscany.com/san-gimignano/accommodation/casolare-di-libbiano.html
Palazzo Malaspina or B&B Giglio inside the walls of a small town with restaurants within walk distance
https://www.chianti.com/chianti-bed-and-breakfasts/palazzo-malaspina.html
https://www.chianti.com/chianti-bed-and-breakfasts/b-and-b-del-giglio.html
Taverna di Bibbiano with its view of San Gimignano
https://www.discovertuscany.com/san-gimignano/accommodation/taverna-di-bibbiano.html
Another favorite:
http://www.discovertuscany.com/san-gimignano/accommodation/il-borghetto.html
Lastly I would plan a week just south of Siena, where you will encounter some of the most “uncontaminated” countryside. Between the soft rolling hills, fabulous vineyards & wine cellars, olive groves, hot water springs and enchanting medieval towns. I would suggest a weekly stay, where you can sit poolside and relax, cook a meal in you kitchen using the great fresh ingredients that you will find the local markets. Be sure to visit Bagno Vignoni and Arcidosso.
Places to look at could be:
https://www.discovertuscany.com/siena/accommodation/farmhouses/casa-podere-monti.html - I love that you can walk into town from here
https://www.discovertuscany.com/siena/accommodation/san-giovanni-in-poggio.html
https://www.chianti.com/wine-tasting/la-lastra-siena-wine-tasting.html not only is this a wine experience, but there is a great little B&B on the property.
Hope this helps you a bit,
Buon Viaggio,
Donna Denise