Late April/Early May the weather Should be warm, but weather is weather. Bring a sweater and for sure a light weight rain jacket just in case. Last year it snowed in the South of Spain on April 25, and that was unheard of!
I stayed in a sweet little hotel that used to be in the RS books in Venice: Hotel Bel Sito and Berlino, which was on its own little square and very close to St. Mark's Square. In Florence, I always rent an apartment, because we usually travel with another couple, but for your second Honeymoon, you'll probably want a hotel. I stay from the train station in any city I visit, because I don't like the people that tend to hang around at night. In Florence, I like the Santa Croce neighborhood, the Duomo (of course) and Oltarno (sp) 'other side of the Arno' River.
Make sure you eat at Mario's in Florence!