Florence is a must, then definitely Siena
Ciao langtangtreks and welcome to the forum!
If this is the first time you visit Tuscany, then I would recommend staying in Florence for sure and if you have enough time, do day trips from Florence to the countryside and other towns in Tuscany, including Pisa and Siena.
The best time to come as far as weather is from April through June and from September to October/November. July and August are peak season and there are more crowds but if you can't come at any other period, those are fine too just be prepared also for some heat ;-).
If you have any other questions, let us know!