Florence is an interesting place to visit at any time as most attractions are open all year round and are indoors!
However, the summer months can get very hot and humid, particularly in July and August.
Therefore, the best times are the spring and autumn months of April, May and June, and September & October, when the temperatures are more favourable
Winter can get cold, particularly January, it can snow, but not often, and you will probably not have to queue for any of the attractions!
Note: many business are closed in August as all Italy seems to go on holiday, although this is now changing with more remaining open.
Christmas, New Year and Easter are busy periods and expensive.
Spring months: March, April, May
Summer months: June, July, August
Autumn months: September, October, November
Winter months: December, January, February