We did a post on our blog about the damage that had been accessed on Saturday here:
http://www.discovertuscany.com/blog/florence/museum-closures-after-heavy-rain-2850/
Pitti closed the main entrance for half a day, but a side entrance was open. Then once windows on the front were fixed, entrance was back through the front... and is all open except for some areas of the Costume Gallery where clothes and other items got wet.
The reports are the storm was really a tornado in some parts of Florence, in addition to the hail. It really was an extraordinary event, nothing quite like it ever before. The post has some more news on things that remain closed, if we hear more places are closed we'll keep updating it to reflect the info we get.
News on Boboli is that it will remain closed until this Friday, Sept. 26... if it reopens earlier, we'll post that. Sorry you didn't see our post earlier, but there really isn't much to be done when the weather intervenes in this way and better to keep visitors out while all the trees are checked to make sure there are no dangling branches. Hope you're in town longer and get to go back, maybe on Saturday!