That's good to know about the approximate mailing date of the next round of paperwork. I'm also trying to finish up my dissertation -- I'm working on a group of 14th and 15th-century sacristy reliquary cupboards and have the most archival work left to do in the Veneto, hence being based in Padova. I wonder how many other art historians have Fulbrights this year -- I understand that they were few and far between last year.
I recently started the housing search in earnest, but I agree that it's difficult to decide on something when we don't really know our stipend amount yet. Last year my friend paid 350 Euros/month on her Fulbright money and she seemed to find that affordable. I had some luck contacting the International Ladies Group of Padova (internationalladiiespadova@yahoo.com) regarding possible housing. Since Verona isn't far away, you might check with them to see if they could put you in touch with a living situation.
I'll be back in touch here when I get my grant forms. Best of luck getting ready!