Another vote for allowing more time to Florence. I'll probably receive a sound flogging for this but with only a couple of days, and galleries not being high on your list, I'd skip the Uffizi and Accademia entirely. I'm an art-lover who would not have dreamed of doing that but I also understand that it's not everyone's thing. Instead, do some of the churches. Along with being good bargains (a fair number are free; others have small entry fees) they're all architecturally different, and you can take in a bit of Renaissance art in situ (in its original place) besides. The context can make paintings and pieces much more interesting than if they'd been removed to a gallery.
I love architecture as well, and there are oodles of wonderful structures in Florence. Museum-wise, you might enjoy the excellent Bargello, which is located in a former 13th-14th century palace/prison. The church of San Miniato al Monte above Piazza Michelangelo is even older, and affords a wonderful view over the city. The duomo, IMHO, is more interesting outside than in but the interior of the nearby 11th-14th century baptistry is a marvel. Palazzo Vecchio is at its Medieval best when looming over Piazza della Signoria at night. My favorite piazza? Lovely little Piazza Santissima Annunziata with its church of the same name (nice frescoes), Brunelleschi's Ospedale degli Innocenti, and eyeful of his greatest achievement - the duomo's dome - from the south side of the piazza.
The list goes on! So don't shortchange this one if architecture is high on your list?