I just looked at Hotel David on booking.com. (It does look nice!) and there's one twin room left on the site for $908 + € 6.00 City tax per person per night for 3 nights so abt. $336 a night. The location, however, is a bit far from what I'd call a central location. IMO, it would be a long-ish walk for your mother from there to many of the more visited attractions and back, not that public transport isn't an option but.... I'm also taking into account that she'll be on her feet for long periods of time at those attractions so, well, I think you'll want to be closer in to shorten your walk distances. You can pretty much figure on the cathedral as roughly the city's center.
I think prices in Florence have less to do with Jubilee as high season rates these days in one of Italy's most-visited cities. Varenna is also very small and has become very popular; it wouldn't take much for most accommodations to fill up in advance. I saw that someone made mention on the forum back in Sept. of booking their hotel 12 months in advance of their stay this past Sept. so stay on top of it!
