So the question is 'not the most obvious things...'
Siena, in the main palazzo, there is a gelateria, if it is summer, get the fig and ricotta gelato.
Florence - Across the river is a good idea, pitti palace. this is an amazing picture gallery. A bit out of the way and up teh hill is San Miniato al Monte. Its one of those places the Italian tourists go to. Capella Medici....where else can yo go to a room with 4 Michealangelo statues?
Venice - scuola grande di san rocco...second the Guggenheim...chill neighborhood. Look for the little round cream filled pastries. The vaporetto down the main canal. Or a ride to Lido or Murano. You are a boat guy, right?
Not off the radar, but in all the cities you mention there is no more of a must see than the Uffizi. Buy your tickets online a month or two before you go and plan your day around it. I cannot stress this enough...this place is incredible...and reasonably sized.
The Palazzo Barberini is one of my favorite places in Rome...low key, uncrowded and major works by Caravaggio. Another is the Doria Pamphilli where yo can see perhaps the greatest portrait of all time, Pope innocent X by Diego Velazquez. there is a very cool tea room at this museum to end your site seeing day and contemplating where to go for dinner.
In each area, ask your hotel person if there are any local fairs or special events going on...