I have two suggestions:
Florence: Hotel Europa, Via Cavout 14
055-239-6715
Have not stayed here but a couple of UA employees that I know highly recommend it.

Venice: There's a really great Best Western on the Canal near the Doge Palace (like steps away). It's in a renovated artist's house. A total find. Can't remember the exact property name and of course the BW website is down. As four/five star 'snob', I was skeptical upon booking (during Film Festival week everything notable was booked) but I really liked this place. Clean, charming, yummy complimentary breakfast and walkable to everything. Get the uppermost room looking out three ways into Venice.